The 25-year old will land in Glasgow on Sunday January 24after his trip was delayed so he could remain with the Glory for a busy schedule of matches which includes a midweek away fixture against Adelaide United tomorrow night.
Hoops boss Tony Mowbray is keen to have a look at Pellegrino but the decision by the Glory to let him go for a trial was put back because the club were keen for him to play during the busy mid-January schedule.
"He [Pellegrino]'s asked if he can go on trial and we've said yes but it has to fit our time frame," said Glory owner Tony Sage. "They [Celtic] had wanted him over this week but he would've missed three games so we said no. Now he's scheduled to go after the Wellington game (on Friday January 22)."
Pellegrino was the Glory's Player of the Year last season after joining the A-League club from South Australian outfit North Eastern MetroStars. Prior to that he enjoyed a stint in Europe with Greek club Panachaiki in 2005 and 2006 after beginning his career in the old National Soccer League with Adelaide City and Adelaide United.