Without a contract, other clubs are free to offer him the chance of Champions League football, or an opportunity to build another project with more favourable resources.
There's also the chance he might just take a break from the game, arguably becoming a more valued manager as he sieves through games as a Premier League pundit.
Of course, the majority of Evertonians will be hoping he fancies one final go at landing a much-coveted trophy with them, and signs a new deal.
While his future in the game remains unknown, for now, here's a look at Moyes' premier accomplishments achieved during his 11-year stay at Goodison Park.
Everton appointed David Moyes as a club staring at the genuine prospect of relegation.
Sitting on just 30 points from 29 games, the Toffees were level on points with Bolton Wanderers, who sat two places below them in the relegation zone.
The club had accumulated just seven points from their last 13 games and seemed destined for the cold, harsh reality of tier-two football for the first time in several decades.
The appointment of Moyes seemed a bold choice, especially since the Scot was unfamiliar with the Premier League, having only managed at Preston.
However, thankfully for the Toffees, he managed to galvanise a beleaguered squad and lead them away from the dreaded drop zone, sealing three wins in his first four games.
That helped the club rise to a far more secure 15th-place finish and beat relegation by a convincing seven points. No mean feat given the uninspiring, aging side he inherited.
So far, the pinnacle of Moyes' career in charge of Everton has undoubtedly been his momentous fourth-place finish in 2005.
Having surrendered Wayne Rooney to Manchester United without being able to sufficiently replenish his squad, Moyes' side started the campaign as a hot tip for relegation.
The roster was thin, the personnel bland and the 4-5-1 approach, on paper, seemed unimaginative and overly defensive.
However, possibly inspired by a dose of siege mentality, Moyes' troops rallied to produce one of the more surprising, unexpected seasons in Premier League history.
The Toffees amassed 61 points, their best tally for 10 years, pipped Liverpool and upset the general monotony of the top four places.
Sadly for the club, this only resulted in a qualification berth for the Champions League, which Everton were unable to negotiate past, although the league finish alone was a miraculous achievement.
Whether or not David Moyes has a better squad now, or has had at another time during his tenure, 2007 to 2009 were probably his and Everton's best years.
During that trio of seasons, the Toffees secured two fifth-placed finishes and another in the top six, as Moyes helped cement his side's reputation as the best of the rest in the Premier League.
Those campaigns also brought his and Everton's highest points totals during the Premier League era, with 65 points taken in 2008 and 63 the year later. Totals that have often been enough to secure Champions League football.
There were also some memorable forays into the Europa League, most notably in 2008, when Fiorentina knocked the Toffees out of the last 16 on penalties.
If Moyes is to move on from Everton, he is likely to look back on this period and wonder how far just a small slice of investment could have taken his side.
A slur that has dogged Moyes for much of his tenure at Everton has been his lack of silverware, and the closest he's ever come to claiming some was undoubtedly 2009.
The Toffees had already progressed through an especially stern FA Cup draw, sending European contenders Aston Villa and Liverpool out of the competition, before facing Manchester United in the semifinals.
When Moyes' side then managed to bypass Sir Alex Ferguson's lineup, via a penalty shootout, it seemed destiny may just be on their side.
However, the Toffees then faced a strong Chelsea side in the FA Cup final, determined to land a trophy for their temporary manager, Guus Hiddink.
Everton scored within a minute of kick-off, again prompting suspicions of fate being with them, before Chelsea's impressive team took hold of the game and secured a 2-1 win.
Moyes will certainly rue the "Runners Up" engraved on his medal that day, but given their arduous path to the final, it was a memorable cup run.
There is certainly substance to the argument that Moyes' lack of silverware is a reason to taint his reputation; however, there's no denying the formidable job he's done with the Toffees regardless.
The issue with a list like this is that it requires his achievements to be physical, when most of Moyes' aren't.
He has taken an aging side on the brink of relegation and transformed them to a valuable squad continually competing for Europe and even on the cusp of the Champions League.
If Everton do finish sixth this season and unluckily miss out on Europe again, Moyes will have had four campaigns where his side have missed out on European football by one place, to go with the four qualifications he's made.
That's not a bad return from 11 seasons, especially given his lack of financial support.
The fact he also operates with just the 11th best budget in the Premier League makes him responsible for continually steering the top flight's primary overachievers.
To truly establish himself and perhaps be accepted among the upper echelons of managers, clearly a trophy will have to be won at some point. However, the overall job Moyes has done at Everton is impressive enough to demand respect on its own.
The big question now is whether he will extend his stay in an effort to achieve that silverware with the Toffees.