The France international is a reported January transfer window target for Liverpool manager Brendan Rodgers as he looks to bolster his goalscoring options.
Liverpool have already added Chelsea striker Daniel Sturridge to their ranks, but Gameiro has been linked with a loan switch to Anfield to provide further support for Luis Suarez.
The Uruguyan has scored 13 of Liverpool's 31 goals in the Premier League this term, and has been the only senior striker available to Rodgers for the entire campaign.
Gameiro, who joined PSG from Lorient in the summer transfer window of 2011, is reported to be available having made only 12 Ligue 1 appearances this season.
The 25-year-old, however, has no ambitions to leave PSG and would rather remain in Paris and try to force himself into Carlo Ancelotti's team alongside star man Zlatan Ibrahimovic.
"I have already told everybody that I am a Paris St Germain player and I hope to remain so until the end of the season," Gameiro told RMC.
"I was lucky to score some goals in the first half of the season and I hope that kind of form will allow me to get more first-team opportunities."