Speaking to HeartsTV ahead of the St Johnstone game, he admitted the search is “difficult” with Souttar being a “top player” and someone “everyone in the dressing room loves”.
“We know that’s going to be hard," he said. “We’ve been looking for centre-backs. We’ve been trying to see if we can find someone and that search will go on.
"Even before John was agreed to the club that he was going to, we knew we had to keep an eye on that market.
"We are looking and we will see what happens, if it is this window or the summer.”
Savage also hailed the role of manager Robbie Neilson in the extension of player contracts.
The sporting chief explained the process of negotiating with Craig Gordon, Michael Smith, Craig Halkett and Stephen Kingsley all agreeing new deals across the past three weeks.
“The manager is key to that," Savage said. “Robbie will have the players in, he’ll speak to them, have a feel for them. See where they are at, what they are thinking. He’s got a good relationship with all the boys.
"He’ll come to me and say ‘look, Craig Gordon or Stephen Kingsley are saying this’ then he will say to me ‘can you go speak to the agents, find out what they are saying to it’. We’re on board with that, we always talk about that.
"Sometimes you want to wait to see how well they do, how they adapt to the league. Other times you know they may be an asset so we need to get them tied up.
"I think we opened dialogue with most of them in September/October time.
"The one thing I do in negotiations, I don't put any pressure on them. I don’t say ‘you need to sign tomorrow or you need to sign next week’. It’s like ‘here's our offer, go away and have a think about it, speak to your family, speak to your agent and come back to us’.
"We're here to negotiate, that’s the biggest thing.”