Morrell was yesterday scheduled to return to Pompey training having been handed a 10-day extended break following his Wales exertions.
It also allowed more time for the midfielder to recover from the broken toe sustained against Holland in the Nations League some three weeks ago.
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Cowley must now assess whether the 25-year-old is ready to feature for 45 minutes against the Hawks.
While the Blues travel to Gosport Borough on Sunday for another friendly ahead of flying out to Spain (July 4) for a week-long training camp.
Cowley told The News: ‘Joe was given a slightly extended break, just because he’d had such a busy summer with Wales.
‘He broke his toe, but it was a clean break and he’s fine. He will be able to train with padding.
‘With Denver and Reeco, we hope to see them by the middle of pre-season. They should be training with the group in Spain again, all being well.
‘Denver has been on the grass for two weeks now, he’s in the early part of his rehabilitation following a prolapsed disk in his back.
‘With the Havant game being on Astroturf, you have to be a bit cautious with some of the players, so we’ll be having a look at that.’
Hume, who arrived from Sunderland in January, missed the last seven games of the 2021-22 campaign through injury.
Meanwhile, Hackett has been sidelined since rupturing the lateral ligament in a knee during February’s 3-3 draw with Fleetwood.
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