Heskey is tipped to be Bruce's first signing, but he insists there is no rush to add to his newly-inherited squad.
He said: "I know there is a clamour for new faces, and what I would say to Hull City fans is there will be, but we have to be patient and take our time.
"The top priority is to analyse the squad, and when we get to work on July 2, everybody starts with a clean bill of health.
"I am coming in to assess everything. The obvious one is a goalkeeper, and it doesn't take Einstein to work out we need one.
"We will look and analyse the squad, try and make some adjustments and hopefully improve it to get where we want to be."