The La Liga side are urgently searching for a replacement for Manchester City-bound striker Alvaro Negredo.
The Spain international is set to link up with former-teammate Jesus Navas at the Etihad Stadium after agreeing personal terms on a move to the Premier League.
Liverpool and Arsenal have both been mentioned as suitors for Gameiro, but French reports - carried by talkSPORT - claim he's committed to join Sevilla instead.
The 26-year-old made the switch to PSG from Lorient two years ago, but has been frozen out following the arrivals of Zlatan Ibrahimovic, Ezequiel Lavezzi and more recently Edinson Cavani.
The report claims he's all but certain to move on following the capture of Napoli forward.
The diminutive France international has a sensational goal record in Ligue 1 - averaging just under a goal every two games.
But he made just seven league starts as PSG won the title last season, as Ibrahimovic and Lavezzi were preferred by then-PSG boss Carlo Ancelotti.
Despite the change of manager - PSG are now coached by Laurent Blanc - it seems Gameiro will still quit the defending French champions.
And he will ignore Premier League interest from Liverpool and Arsenal to lead the attack for the Andalusian club.