The free agent is currently mulling over a two-year deal as the Blues attempt to head off interest from rival clubs.
The former Manchester City midfielder has reiterated to Michael Appleton his desire to remain at Fratton Park following his time at the club on a short-term deal last season.
Last week he turned down Barnsley, while Bradford have also been linked with a move for the 23-year-old.
For Appleton, though, the wait goes on for Etuhu to pledge himself to the club on paper.
He said: ‘At the moment, Kelvin has been made an offer and it is up to him to come back with his representative.
‘He’s not had anyone really looking after him since he has been at the club so he now has an agent.
‘I spoke to him last week and he seems quite keen to stay and desperate to continue working with myself.
‘Hopefully, something can be sorted in the next week or so. I have not given him a deadline.
‘I don’t want players here if they are not keen to come and play. If they want to go elsewhere, good luck to them.
‘But I am hearing he has turned down Barnsley and he wants to stay with us.
‘And I believe you have got to take him at face value.’
Meanwhile, Pompey are also waiting on a contract answer from Marko Futacs.
The Hungarian striker has been offered a 12-month deal on reduced terms.
That is in line with driving down the wage bill for life in League One next season.
Futacs and Etuhu are the only two senior players who have been presented with deals.
The remainder of Appleton’s squad are effectively up for sale.