Caldwell's current deal expires at the end of next season and Mowbray plans to open talks with the Scotland defender as soon as he returns for pre-season training at the beginning of next month.
Mowbray, who was Caldwell's boss at Hibernian, said: "I will speak to Gary soon about his contract situation - the first chance I get, I will do that.
"I will talk to him, his advisors and to chief executive Peter Lawwell about it.
"I will see where we are at because I am sure he has been approached before now on a new contract. I assume he has.
"I have not tip-toed into the issue as yet, but I will see what Gary thinks.
"He might have huge aspirations to move to the English Premier League, I don't know.
"I will assess his thinking and see where we go with it."