"We have a lot of names on our list and it is now a case of doing our homework and trying to get the best players who we feel would help strengthen our squad for the step up to the Premier League.
"Lee McCulloch is certainly a player who would fit the bill for the type of player we are looking at but we don't even know if he would be available.
"He did really well for Rangers and as far as we are aware he is happy up there and, as I said, I don't even know if they would be prepared to sell him."
Stoke have also been linked with the Gers' wantaway striker Daniel Cousin, but Rudge has ruled out a move for the Gabon international.
"We have a list of players and I am in regular contact with the manager and Daniel Cousin is definitely not on our list," he added in the Daily Express. "We are aware he is available but he is not one of our summer targets."