John Souttar is set to make a return in time for the Scottish Cup Final.
The Hearts defender - who is moving west to join Rangers at the end of the season - has had surgery on an ankle injury that has seen him ruled out since March 5.
The Tynecastle side face the Ibrox side at Hampden on 21 May.
Fellow centre-back Craig Halkett will also be available for the cup clash after he was forced off with ankle damage in the semi-final victory over city rivals Hibs earlier this month.
Neilson rated the duo's chances of making it to Hampden "11 out of 10".
The update was issued by Jambos boss Robbie Neilson during his press conference.
Neilson said: "John is on the pitch now running and building up. Craig will probably be available for the league game against Rangers [14 May] and play a part of it.
"Then the decision will be whether he plays in the final. But both should be available, it's great news.
"For us it's about trying to get everyone as fit and game ready as we can for the final. They will be fit, if we can wheel them out! The only one who will miss the final is Beni Baningime."
Stephen Kingsley and Andy Halliday are back this weekend with Cammy Devlin aiming to return in time for the cup final, too.
Hearts are currently unbeaten in nine matches, securing third place in the Premiership with a European group-stage place already guaranteed for next campaign.
With four league games still to play, starting with a home tie against Ross County this weekend, the Jambos boss is looking for his side to maintain momentum and take every game as it comes.
"We're not thinking about the final yet. We can't go into Saturday with half measures saying we have a big game in three weeks' time.
"After County we face Celtic, Motherwell and Rangers in the league - it's massive games and we can't take our eye off the ball at all." He added.
