Koeman (manager of PSV) has angered Pompey chairmen Milan Mandaric.
Koeman said: ‘I have spoken with Jefferson and I have said to him I do not want to lose him.
‘If the offer came from Manchester United I would recommend to him that he accepts the proposal without doubt.
‘But Portsmouth? I hope he is astute and chooses the sporting subject over the economic thing.’
Mandaric said: ‘When was the last time Ronald Koeman was in Portsmouth?
‘I’ve never heard a player that’s come here say that Portsmouth isn’t big enough.
‘Portsmouth was big enough for Milan Mandaric and Sacha Gaydamak, so it should be big enough for Jefferson Farfan.
‘Coming here would be a good move for Farfan – and I’m hopeful the deal will happen.’
PSV’s sporting director Stan Valckx acknowledged they had received Pompey’s offer for Farfan: ‘If they want to take Farfan they will have to pay what the club requests.
‘Also, we must talk with the player to see what he wishes for his career.’