It is understood the League Two high-fliers were keen on recruiting the out-of-favour keeper for the remainder of the campaign.
However, they failed to reach agreement on the wage contribution for the former Spurs man, scuppering the potential move.
It remains to be seen whether Cheltenham have the inclination to revisit a potential deal during this January transfer window.
Certainly third-choice keeper McGee has no Fratton Park future, with his three-year deal expiring at the season’s end.
The 24-year-old has been available for a move since last summer, a situation which has repeatedly been clarified by Kenny Jackett.
As the Blues’ number one during the 2017-18 campaign, McGee was joint-top appearance maker alongside Jamal Lowe with 50 games.
However, the arrival of Craig MacGillivray and the ongoing development of the highly-regarded Alex Bass has seen McGee drop down the pecking order.
He made five appearances last term, with his last first-team outing arriving in the Checkatrade Trophy against Arsenal under-21s in December 2018.
McGee was subsequently left out of Pompey’s pre-season training camp in Dublin last summer and wasn’t included in any friendlies.
The ongoing uncertainty over his future comes at a time when his rivals are locked in a battle to become Jackett’s first choice.
Bass surprisingly dislodged first-team regular MacGillivray at Gillingham on New Year’s Day, then retaining his place for the FA Cup win at Fleetwood.
Yet the Scot returned to the side for Tuesday night’s 2-1 Leasing.com Trophy success at Walsall.