Swansea City say striker Michael Obafemi has been subjected to "disgusting" online racist abuse after joining Burnley on loan.
Swansea confirmed the matter had been reported to South Wales Police, who have yet to comment.
"Those responsible do not represent Swansea City or the values of our club and community," the club said.
"The club is sickened by the vile language used in the offending posts and is working to identify those responsible and take the strongest possible action.
"There is no place for racism or discrimination of any kind in society or football.
"Ourselves and Burnley will offer Michael every support in this matter."
Republic of Ireland international Obafemi, who has scored 15 goals in 52 appearances for the Swans, has joined the Championship leaders for the rest of the season with a view to a permanent transfer in the summer.