Jenas damaged his achilles in 1-0 defeat to Manchester United on Saturday, with McLeish revealing that parent club Tottenham are set to play a role in the player's recovery.
McLeish told the club’s official website: "I am bound by the fact Jermaine is not an Aston Villa player to reveal any news about him.
"We have left it in the hands of Tottenham and they will probably make a statement later on. So obviously it's not good news.
"I think Jermaine has ruptured his achilles and that will take some time to sort out.
"It's for Tottenham to say what will happen as they are the parent club.
"We just hadn't got started with him at all and it's been very frustrating for both parties. But it must be hellish for Jermaine.”
The manager also commented on the return of Australian midfielder Chris Herd, noting the youngster may feature in his starting XI against struggling Bolton on Saturday.
"Chris has trained, he was feeling his hip. He was just getting a little bit of stress in it due to the amount of running he's been doing,” he explained.
"He's non-stop, the kid, he really puts himself about. I think he's merited a start in the team.
"I think I've needed his energy and athleticism."
Aston Villa are also without goalkeeper Shay Given, after he was ruled out for a month with a hamstring injury he picked up in the United game.