Coventry chief executive Graham Hover has made it clear that trialists Simon Donnelly and Phil O'Donnell would only be allowed to join the club on a pay-as-you-play basis.
McAllister wants to strengthen his squad
Donnelly and O'Donnell, who are both free agents after four unhappy, injury-ridden years at Sheffield Wednesday, will have 10-day trials at Coventry in July.
But Hover has made it clear the Sky Blues are wary of signing two players with a long history of injury problems.
"Given their track records any decision would be made on a pay-as-you-play basis - and that's if it even gets that far," Hover told the club's official website.
"We often have players at the training ground and I'm sure these won't be the only two players that boss Gary McAllister and his coaching staff will be looking at on a trial basis.
But agent Raymond Sparkes is hopeful of a positive outcome.
"Both these players were international team-mates of Gary McAllister's and they are going there in the
hope of winning permanent deals," said Sparkes.
"They are keen to prove their fitness and that their passion and desire for the game is still there.
"Simon Donnelly was wanted in the USA but decided to put that on hold because of Coventry.
"Umpteen different clubs have made enquiries, including Scottish ones, but staying in England and showing what they are capable of is very much at the top of their agendas."