Manchester City insist midfielder Joey Barton "made no offensive gesture" at Fratton Park following the club's 2-1 defeat against Portsmouth on Saturday.
Barton made his England debut earlier in the week against Spain
Barton's challenge on Pedro Mendes led to the Pompey player being carried off.
"The club have not received a complaint regarding Joey Barton's behaviour," said City spokesman Paul Tyrrell.
Hampshire Police will tell the Football Association of an alleged incident involving an unnamed City player but will not hold their own investigation.
The police will instead be liaising with the FA after being alerted by one of their officers.
Midfielder Barton drew the ire of home fans after an aggressive challenge from behind on Mendes just before the break.
He caught the Pompey man on the back of his ankle and was jeered through to the final whistle.
Tyrrell added: "If we get a complaint it will be robustly defended by the club as our own officials were close to the player as he went to thank our fans for their support.
"He made no offensive gesture."
Having drawn level in the second half, City went down to an 81st-minute Kanu goal that leaves them 16th in the Premiership.