"He will be leaving,” Alexander said. “The timeline of when he leaves is not 100 per cent. It's not even been talked about, to be honest.
"We've been told that he's signed a pre-contract at Dundee United and that's as far as it goes.
"It's quite an unusual situation for me because I've never really experienced this before because obviously it's my first stint managing in Scotland.
"The pre-contract, signing for another club in your own league and still playing for the other club, is quite an unusual and unique set of circumstances, so I'm still getting my head around that scenario.
"He will leave but the actual timeline for when he leaves hasn't been decided because we haven't heard from Dundee United in terms of a bid or anything.
"If he's here until the end of the season, we will enjoy having him with us from now until then."
Alexander compared the Watt scenario to that of Declan Gallagher, who signed a pre-contract with Aberdeen last season.
Alexander, talking to Press Box Podcast, added: "We had a similar sort of situation last year with Declan Gallagher, who straight away from January I knew would be leaving, either in January or at the end of the season.
"Once we got to February 1, it was like, right he's leaving at the end of the season.
"We just cracked on. He was as good as gold, he worked hard, he trained hard and he played well for the team but it was slightly different because it was kept in-house.
"I think Aberdeen announced he was signing for them somewhere and it became a bit of a different situation. I don't want our team to be about one player because we know that one player could leave at any particular window."
On the job of replacing Watt, Alexander said the qualities offered by Connor Shields, Ross Tierney and Jordan Roberts proved there was no rush.
"I'm quite comfortable with where we are," he said. "We don't necessarily have to replace Tony from outwith the club.
"I feel we've got the players that will pick up the baton straight away."