But if Morrell was to drop down to League One then the Blues would be his favoured destination.
Cowley remains an admirer of the 24-year-old, having signed him on loan from Bristol City when in charge of Lincoln ahead of the 2019-20 campaign.
Morrell featured in every minute of the Imps' opening six games as they sat second in League One before Cowley made a surprise departure to Huddersfield.
He remained a regular under successor Michael Appleton, featuring 32 times prior to the campaign was curtailed by the Covid-19 pandemic.
The Ipswich-born ace earned a switch to Luton for an undisclosed fee last summer but endured a difficult maiden season.
Morrell made just 11 appearances in all competitions as the Hatters finished 12th in the Championship.
Despite Morrell being on the periphery of things at Kenilworth Road, he's remained a key player for Wales.
Throughout this term, he has won 10 caps for his country. His most recent outing arrived in the Dragons' 3-0 friendly defeat to World Cup holders France, with his display earning plenty of plaudits.
Morrell is hoping for an impressive Euros before returning to Luton for pre-season in a bid to break into Nathan Jones' plans.
Should his situation not change at Kenilworth Road then he's likely to explore his options.
Remaining in the Championship is Morrell's preference given he is a regular at international level.
But if he was to decide to drop to League One then Pompey would be in pole position due to his relationship with Cowley.
Ahead of a renewed promotion push, Pompey certainly need to bolster his options in the engine room.
As things stand, there is no centre-midfielder under contract at Fratton Park.
Ben Close turned down a new deal and is poised to join Doncaster, while Tom Naylor also looks set to depart after being offered a fresh contract on reduced terms.
Meanwhile, Andy Cannon left at the end of his contract while Bryn Morris was released.
The Blues are interested in Scott Twine after opting against extending his stay at Swindon.
Cowley's also sounded out Tottenham about the possibility of Harvey White returning for a second loan spell.