The USA international was reported to be attracting interest from a number of clubs following his impressive displays at the World Cup, and he is hopeful that a decision will be made on his future as soon as possible.
"I know that Fulham has offered to Kansas City and I know that Sunderland put in an offer or are putting in an offer," Besler told Sports Radio 810. "We're trying to get something done as soon as possible. It's a situation which needs to get resolved.
"I want to be staying in Kansas City if I'm going to stay, but if they're going to sell me, then I want to know as soon as possible."
Reports on Wednesday suggested that Sunderland would pay £3m to secure Besler's services.