The former Liverpool and Barcelona playmaker initially arrived at Villa Park in January on a short-term loan deal under Steven Gerrard, whom he played alongside at Liverpool.
A successful spell earned a permanent move from Barca during the off-season, but after Gerrard's sacking in October, Unai Emery took charge at the Midlands club.
Reports emerged earlier this month the 30-year-old was seeking a departure in the January transfer window, but Coutinho has taken to social media to rubbish those claims.
"In the last few days I've seen a lot of news with my name," he wrote in an Instagram post. "The problem is now that some lies have started, and I'm here to clarify.
"Never, and at any moment, [have I] had any kind of conversation asking to leave the club, because I'm happy here and my family [are] too.
"My only focus now that I've recovered from injury is to work at the maximum every day, to play [at] a high level, and help the club and my team-mates to achieve our goals."
It has been a tough campaign for Coutinho so far, with form and injury struggles contributing to him losing his position in the Brazil squad ahead of the FIFA World Cup.
After recording eight goal involvements (five goals, three assists) in 19 Premier League games during his initial loan spell, he has failed to contribute any in 13 league games since the move was made permanent.