The 31-year-old is currently on a season-long loan at Qatari side Al-Duhail, but it has not gone according to plan.
Coutinho has managed just six league starts with a total of 419 minutes so far in Doha.
According to Spanish newspaper AS, his limited game time could see the Brazilian ace be reunited with Messi at Inter Miami this January.
The former Liverpool star previously played with the World Cup winner at Barcelona.
A move to Florida would also see him link up with ex-teammates Luis Suarez, Sergio Busquets, and Jordi Alba.
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Coutinho left Liverpool in a £105million deal in 2018, spending three seasons at Barcelona and clocking up 106 LaLiga appearances.
Both Inter Miami and LA Galaxy are interested in his services, but no approach has made to Villa as of yet.
Villa boss Unai Emery recently touched on the future of the Brazilian.
He said: "Philippe is a very good person and always we have to respect him as a person, firstly. Secondly, as a player, he has played at a very high level.
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"He has not been consistent because of injuries and we decided with him speaking and agreeing with him to try that if something is good for him, and good for the club, and for the squad, we can let him leave. Then he can find his good performance as a player."
A move stateside could help the player to rekindle his form, having lost his spark ever since he swapped Anfield for the Camp Nou.