The Dragons suffered a 4-0 last-16 defeat to Denmark in Amsterdam on Saturday.
Morrell started all four matches for Rob Page's side, with the highlight an impressive display in a 2-0 Group A win over Turkey.
The midfielder on the Blues shopping list during the summer transfer window, with Danny Cowley previously working with Morrell when in charge of Lincoln.
The 24-year-old joined Luton from Bristol City last summer but struggled for opportunities at Kenilworth Road.
Morrell played just 11 times in total and admitted before the Euros started that he wants to be playing regularly ‘at whatever level’ in the 2021-22 campaign.
Now he's set for a summer break before he addresses the upcoming term.
Posting on Instagram, Morrell said: ‘Obviously gutted with how it ended last night but it’s the proudest moment of my career to have represented @fawales at a major tournament.
‘Thanks for all of your support from the stadium and from home, it means everything to us and we can assure you that we’ll do everything we can to come back stronger.
‘Time to rest up now and see what next season brings’
Pompey have signed midfielders Shaun Williams and Ryan Tunnicliffe so far this summer – from Millwall and Luton respectively.