Reds boss Brendan Rodgers is looking to bolster his striking options at Anfield in the January transfer window after a lack of goals in the first half of the Premier League season.
And, despite the imminent arrival of Daniel Sturridge from Chelsea, Rodgers has also been linked with a move to sign Gameiro on a loan deal until the end of the season.
However, the 25 year-old, who scored 14 goals for PSG last season following a £9million move from Lorient, is determined to remain at the Parc des Princes.
Head coach Carlo Ancelotti has used Gameiro sparingly this season with Zlatan Ibrahimovic, Ezequiel Lavezzi, Peguy Luyindula and Guillaume Hoarau all vying for first-team action.
But the player is not ready to leave PSG just yet, telling radio station RMC: "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.
"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."