Michael Appleton is to offer the free agent a two-year deal after he impressed during his short-term stay on the south coast.
The 23-year-old Etuhu has already indicated he would consider staying with the Blues as they prepare for life in League One.
But Barnsley and Bradford are also reportedly eyeing up a move for the ex-Manchester City man who is looking to rebuild his career following a spell in prison.
Appleton, though, remains confident Pompey are in the box seat.
He wants the talented midfielder to spearhead his League One plans as he looks to rip up his squad and start afresh.
Etuhu is one of just two senior players to be offered deals for next season – the other being Marko Futacs.
And the Blues boss is hopeful of capturing his signature as he looks to put the blocks into place for a new era.
He said: ‘I am going to be making Kelvin an offer over the next 24 hours – if I can get hold of him!
‘Seriously, I believe he is on holiday at the moment so it is a case of getting him at the best time.
‘It will probably be a two-year deal and, hopefully, he will accept that and is ready to stay with us.
‘I think he has proven his worth since we gave him an opportunity and he helped push us hard in a difficult end to the season.
‘It’s something I would like sorted out quickly and Kelvin has indicated to me he would like to stay with us.’