Victory in the north London derby is a must in this regard. The Gunners are currently two places above Tottenham, with a six-point advantage and a game in hand.
If Sunday's match and the rest of the season plays out more or less to recent form, though, Spurs could end up the furthest behind their rivals they have been in five years.
Arsenal's own peripheral position in the battle to win the Premier League in recent campaigns has made finishing above them a tangible target for Spurs. The derby element, coupled with league table proximity has added extra spice to their meetings and an even greater desire to watch the other slip up elsewhere.
Despite the disappointment of missing out on Champions League football these last two years, after finishing one point behind Arsenal on each occasion, the closeness hinted at Spurs finally gaining ground on them in something close to consistent fashion.
The difference between the two clubs so far this season is the very factor the Lilywhites are likely going to require to overhaul their neighbours anytime soon: stability.
Spurs not only changed manager midway through the current campaign, they also instigated a substantial remodelling of their playing staff last summer (one more notable than most realised at the time).
Both decisions could still pay off down the line. For now, it has left Spurs trailing an Arsenal side comparatively reaping the benefits of a settled and talented squad familiar with their manager's demands.
Long-time boss Arsene Wenger is well aware of how important stability has been to his plans and of what such breathing space could mean for Spurs' latest manager Tim Sherwood:
As reported by The Independent's Sam Wallace, Wenger went into some detail about the need for patience in such matters:
I’m always pleading for stability. Maybe you could say I’m pleading for myself! I always think technical stability is important. But it becomes more and more difficult because in every single game there is a trial taking place, based on what the manager has done right or wrong. The stability will certainly be much more difficult.
I don’t know Sherwood as a coach. I knew him as a player because I am a long time in this job. I like the fact that he has learned his job and gets his chance. In England you rightly complain that young managers don’t get a chance. When you get one you have to support him.
Wenger's "stability" is his word for what some Arsenal supporters and critics might regard as complacency and being too comfortable.
Their Champions League exit and inability to make the most of their time at the top of the table this season perhaps backs up their belief he has stayed in the job too long, though not all would agree, especially with the league title still possible and an FA Cup semi-final ahead.
While Wenger has not delivered enough success for the Gunners of late, their consistent Champions League qualification is certainly enviable for aspiring Tottenham. This season specifically, the Frenchman has put together his most competitive team for some time too.
The introduction of £42 million man Mesut Ozil was the headline move. But in fact, the key elements have been the consistency of the Laurent Koscielny and Per Mertesacker-led defence, Aaron Ramsey repaying his manager's faith in him, and the experience now accumulated by earlier foreign imports like Santi Cazorla and Olivier Giroud. Essentially, pieces Wenger has been able to put in place over time knowing his job was safe.
At White Hart Lane, Sherwood was the sensible option to become manager once it was decided Andre Villas-Boas' services were no longer wanted. Yet, with the team enduring a mixed bag of results recently, his long-term suitability is still up for debate.
Perhaps someone like current Netherlands manager Louis van Gaal—still being linked with Spurs by ESPN.co.uk, among others—might have the capacity and nous to implement substantial improvement short-term.
More realistically, though, whoever is in charge at Spurs is unlikely to succeed without more than a year or two to get things in order. Even then, overtaking Arsenal as a force in the Premier League will not come easy.
Few coaches are granted luxuries of time and patience anymore. Wenger and Arsenal's own generally good health is testament to what can happen when a club sticks with someone.