The Mirror says the 24 year-old will be allowed to leave if Portsmouth match Mallorca's asking price as Redknapp wants to make a push for the UEFA Cup.
The deal is complicated as the Spaniards are holding out for a big fee as they will have to pay 50 per cent of any transfer to Gutierrez's old club, Newell's Old Boys.
Gutierrez said: "I know the situation and my position has not changed. If the offer is right then I would like to play in the Premier League.
"I am convinced I could be a success for a club like Portsmouth and am ambitious to succeed.
They have a very good reputation and want to be successful so it is a club that appeals."