Hird said nothing was confirmed with Thompson, who left Geelong last month citing burnout after more than a decade as senior coach.
He also said he last spoke to Thompson a couple of weeks ago, and hoped his former teammate would still agree to return to the club where he made his name as a player.
"To my knowledge there hasn't been a contract signed," Hird said on Monday morning at training. "I know Mark's on a break at the moment and we're respectful of that.
"It's something the club is working through and when there's something to talk about, we'll talk about it.
"At the moment it's pretty obvious there's been speculation about what's going to happen and that's all it is at the moment.
"I'm not sure [when the coaching staff will be finalised] but we've got a bit of space left so we'll see what happens."
The Bombers ran through the first of many sessions at their new summer training ground at Penleigh and Essendon Grammar in Melbourne's northern suburbs on Monday morning.
Veteran defender Dustin Fletcher, fresh from his stint at Australia's goal keeper in the International Rules Series played in Ireland last month, was in full flight alongside other experienced heads Mark McVeigh and Andrew Welsh.
The club's rehabilitation group was remarkably small with just Tayte Pears (foot), Taite Silverlock (foot) and Anthony Long (hamstring) kept away from the main group while David Myers was restricted to static drills as he was wearing a moon boot.
Bachar Houli was a notable absentee after his botched attempt to secure a trade to Richmond during last month's official exchange period.
"We'd love Bachar to be here on the list but he's made a decision that he doesn't want to be," Hird said.
"You cut your ties and you move on. We're a proud club and a club that's moving somewhere and if he doesn't want to be part of it, that's his decision."
Houli is expected to enter the NAB AFL Pre-season Draft, where he is expected to make his way to Punt Road.
Hird said his first pre-season as coach of his former club had been progressing well so far.
"The boys have been back for a week and a half now and their fitness is really good," he said.
"They're training well and we just need to get through to Christmas training hard and teach them how to play football.
"We've had a lot of intense teaching sessions already in the two weeks we've been going and I think they've learned a lot.
"They've already showed a willingness to play the style of football we want them to play."
