The midfielder was a standout for the Jags in the opening months of the season but saw his campaign come to a premature end when he was crocked in the abandoned tie with St Johnstone in December.
Osbourne penned a one-year deal at Firhill last summer and Archibald is eager to retain him if he can return to full health as he continues his recovery from an ankle injury.
He said: "We need to see if he is fit. We have invited him back for pre-season but whether he wants to, with the situation with his family down south, I'm not sure.
"It would need to be appearance-based or something like that or we will wait and see how he is in pre-season and then offer him something. A fit Isaac Osbourne, we would have him all day long.
"We can't afford to carry players. To be fair to Ozzy, he played and trained all the time and was fit until the St Johnstone game, which shouldn't have been played. He was a massive loss for us."
Archibald has already begun shaping his Jags squad for another crack at the SPFL Premiership next season, with defender Lee Mair being cut loose. Keeper Paul Gallacher, Steven Lawless and Christie Elliott have been offered fresh terms.
Archibald said: "I would be surprised if bids came in. A lot of them are tied up.
"A lot of managers say to me after games that they like players, we get that a lot. But I don't think there is anyone who would pay money for anyone."