The centre-back will be sidelined for up to four weeks with a hamstring complaint.
Downing suffered his setback in Tuesday’s 5-1 defeat at Peterborough as the Blues went out of the Papa John’s Trophy.
The former Doncaster and Blackburn defender has been fourth-choice in central defence this season behind Jack Whatmough, Sean Raggett and Rasmus Nicolaisen.
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Downing’s made only six appearances and hasn’t played a league game since September 2019.
However, his fitness may mean those clubs look elsewhere. Potential suitors could want someone already up to speed and able go into their starting XI straight away.
Pompey boss Kenny Jackett said: ‘Paul will be out for 3-4 weeks with a hamstring injury.
‘He was playing against a real high-level Peterborough side and hopefully in a month, he will be fit.
‘We haven’t had anything on the table for him, whether that changes we will see in the next two weeks.
‘But, you’re right, if they did, it would take somebody a couple of weeks to get him match fit, which isn’t too long.’
Downing arrived at Pompey on a free transfer in June 2019, signing a three-year deal.
He was earmarked as a regular starter at the beginning of last season and featured from the outset in the opening six League One games.
However, his final third-tier appearance arrived in a 2-2 draw with Burton.
He fell behind Raggett and Christian Burgess in the pecking order, while Oli Hawkins, Tom Naylor and James Bolton were used as makeshift centre-halves ahead of him.
It’s understood Pompey aren't pushing the West Brom academy graduate out of the exit door but will work with Downing if there’s a move he fancies.