The Australia international is back in training after a hernia operation but the Hoops boss hinted that talks about the striker's future had reached an impasse.
"I won't sit here and deny there have been conversations with Scott and they have been interesting chats but at the moment there is nothing to say either way," Mowbray said.
"Scott is at Lennoxtown (Celtic's training ground) working very hard to get fit for Tuesday but we will wait and see.
"Scott is looking for assurances, he wants to play and be on that field every minute of every game scoring goals.
"He does understand that I have a squad of players but he wants to play.
"I can't assure him he will be on the field for 90 minutes of every game, because I've got respect for the other players and that's why you have a squad.
"He is obviously a talented boy who has scored goals for the club over the piece but no player gets guarantees that he will play 90 minutes of every game.
"Would I like to keep Scott McDonald? Yes. I want as many good players as possible for me.
"Would he like to stay? Yes, I think he would because it's a great club with great supporters, a great history and he has scored goals.
"But there are three, four, five little pieces that make up the whole pie and some of them are pretty big in Scott's mind and important in what might happen."
The turnaround at Celtic continued on Friday as Stephen McManus completed his loan move to Middlesbrough while left-back Danny Fox signed for Burnley.
Mowbray rejected outright speculation that he is interested in Hearts left-back Lee Wallace but was less strident about claims Celtic were in for Real Mallorca defender Ivan Ramis.
However, he is confident new faces will arrive at Parkhead before the transfer window closes.
He said: "There is a little bit of business getting done and hopefully there is a little bit more in the next few days."
Celtic go into Saturday's Clydesdale Bank Premier League clash with Hamilton at New Douglas Park 10 points behind Old Firm rivals Rangers at the top of the table.
Mowbray tried to remain philosophical about the criticism which intensified following the 2-1 defeat by Hibernian at Parkhead on Wednesday night.
"I don't get annoyed," he said.
"I don't think the criticism will ever die down.
"As soon as you draw a match there is criticism. I understand the agendas of having to create a divide in this city, to make sure that there is something to write about.
"There needs to be some divide somewhere, there needs to be an unhappy footballer or something not quite right.
"All I am doing is trying to build a team, to put the foundations down for longevity of success."
The former Hibs and West Brom boss reiterated his belief that Celtic can close the gap over the Ibrox men.
"Why not?" he said.
"There are enough games and we will be fighting for every point available.
"We've got to play Rangers twice and we have a game in hand.
"Potentially there is a point between us. Are you saying one of us isn't going to drop a point along the line?
"The league is there to be played for and while you can contest it, you've got to believe that you can win football matches.
"Hopefully we will come out of the transfer window with a team that will win game after game."
On McManus's loan move, Mowbray said: "My conversation with Stephen this morning was about him getting some football.
"He wants to get into the Middlesbrough side and if he comes back, he will come back a confident guy ready to play Champions League football.
"If he likes it and Middlesbrough like him and there's a deal to be done, then it's a time to talk about (a permanent transfer) then."
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