Reports have claimed that Harry Redknapp wants to sign the winger in a £4.7million deal.
Gutierrez, who has three years left on his Mallorca contract, would also see his wages tripled by a move to Fratton Park.
"I only know the news that has appeared in England," Gutierrez told the Spanish media. "My work is in Mallorca and not in the rumours in the press."
Mallorca have confirmed no bids have been received for Gutierrez, who linked up with the Primera Liga side two years ago.
And Mallorca coach Gregorio Manzano outlined his intention to fend off any interest in the exciting wide man.
Manzano said: "Jonas is important for Mallorca and will not leave the club."