It is understood Danny Cowley would be keen to reunite with the midfielder at Fratton Park, having worked together at Lincoln.
Morrell, 24, endured a difficult maiden season at Luton after joining from Bristol City for an undisclosed fee last October.
He played only 11 times in all competitions as the Hatters finished 12th in the Championship.
The likes of Kiernan Dewsbury-Hall, Pelly Ruddock and Luke Berry were ahead in the pecking order at Kenilworth Road.
Still, Morrell remains a regular for Wales and is expected to play a prominent role in their Euros campaign starting on Saturday against Switzerland.
The ex-Cheltenham loanee revealed he's left his future to his representatives while he's away with the Dragons.
After a frustrating 2020-21 campaign, he wants to be featuring week in, week out next term – although it is understood he'd rather that be in the Championship than drop to League One.
Morrell recently told Sky Sports: ‘Addressing next season is something that I hope is hopefully under way.
‘It’s something that I’ve sort of put of my mind and left with representatives and people over the summer.
‘I’m focusing on the Euros and whatever happens next season happens.
‘It's definitely been a frustrating season for me and it didn't go to plan for whatever reason.
‘The chance of regular Championship football was what I wanted, but I do feel fit and 100 per cent ready to go for that first game.
‘When I get that red shirt on I have an extra spring in my step.
‘I will focus on the Euros now, but I want to play regularly at whatever level and I will address that next season.’
Pompey have made only one signing during the summer transfer window so far.
Liam Vincent arrived from Bromley for an undisclosed fee last week, signing a three-year deal.