Although Roberto Martinez has already come out and said that Coleman is not for sale, he is a player Moyes knows well, and at the age of 25, he may feel it is time to move to a bigger club.
Whereas the signing of Mesut Ozil for Arsenal last summer galvanised their squad, the arrival of Juan Mata has not had a similar effect on a demoralised United squad, recent UEFA Champions League comebacks aside.
Coleman is good but not great. He will strengthen a good team but not drastically improve its fortunes.
If reports are true that Coleman will command a fee of £15 million, Moyes should reconsider. To rebuild his United squad is going to take a monumental effort. Existing squad players need to improve their game or be moved on, and new blood needs to brought in across a variety of positions.
It must be said, of course, that it is too early to condemn Moyes for his overall transfer policy this summer. Clearly he understands there is a need to improve even after their recent win over Olympiakos, as these quotes, per ESPN, after they had qualified for the last 16 demonstrate:
I think the club itself needs to be classed as one of the favourites but I think we all know we as a team have to improve if we are to keep progressing in the competition.
However, Moyes' transfer history at United is mixed. The signing of Marouane Fellaini last summer has been underwhelming, and whilst Mata was considered to be a huge coup for United at the moment, he is taking time to adapt to his new team.
This is partly because he lacked game time at Chelsea but also because Moyes is not playing him in his favoured position just behind the strikers. All of this suggests that Moyes is not quite sure how to solve his on-field woes.
Up front United have two world-class forwards in Robin van Persie and Wayne Rooney, as well as useful back-up in Danny Welbeck. Rooney can also play in midfield, and combined with the attacking prowess of Mata and the exciting Adnan Januzaj, United have the potential to worry the best teams in Europe.
Still they lack depth in the top half of the pitch.
Shinji Kagawa has never flourished since his transfer from Borussia Dortmund, and Antonia Valencia, Ashley Young and Nani are inconsistent at best.
So if any of the more exciting rumours—Metro has linked Marco Reus with a move and also claims Toni Kroos is considering United, while the Daily Star claims Edinson Cavani is on the radar—turn out to be true, this could turn United into a consistently dangerous team.
More importantly, Moyes needs to add strength and technical ability to his midfield, whether this be through a new signing, the returning Darren Fletcher or by somehow rejuvenating Fellaini.
Despite his protestations, Tom Cleverly is not the answer. The fact that 40-year-old Ryan Giggs was able to add so much quality to United in such a crucial game demonstrates, with no disrespect to the great Welshman, how sorely improvements are needed in this area.
Would Seamus Coleman be a good signing for Manchester United?
The departing Nemanja Vidic and ageing Rio Ferdinand present both a problem and an opportunity for United.
For too long, players such as Phil Jones, Chris Smalling, Rafael and Johnny Evans have swapped places, with only Evans really cementing himself as a solid centre-back for the team. Jones and Smalling both have potential but are used almost as utility players when a regular back line would be preferable.
Ideally United should look for a world-class centre-back of the calibre of the departing Vidic to shape their defence around.
Whilst Coleman would be a big improvement on Rafael, there needs to be money left for improvement in other areas.
A talented forward or supporting midfielder, a solid central defender with the ability to both break up and create attacking play and a completely reorganised back line are needed for Moyes to restore United's indomitable spirit.