McGrath, who turned 34 on Monday, has not played a Test since the July home series against Bangladesh because of ankle trouble and is desperate to try and play for New South Wales (NSW) in his bid to return to the national side.
Australia's premier fast bowler failed to prove his fitness for a NSW second XI match against Tasmania's second XI, which started in Hobart on Monday, and will now aim to make his comeback for a domestic One-day match against South Australia on Sunday.
But with the Australian Test squad for the Sri Lanka series to be named on February 20, McGrath has just that match and a Sheffield Shield game against South Australia starting on Tuesday to show selectors he has put his injury behind him.
Hohns conceded McGrath was running out of time to prove his fitness and that he may be too ambitious by aiming to play in the first Test in Sri Lanka, starting in Galle on March 8.
"He's got to get back on the field and as yet that hasn't happened so time is running out, there's no doubt about that," Hohns said in Melbourne on Monday.
"It's an injury that's taking quite a while to heal, there's no doubt about that and Glenn right now is desperately trying to make himself 100 percent fit before he plays a game."
Warne and McGrath raring to go