A United scouting delegation was reported to have been in Zenica on Friday, where they watched Begovic help Bosnia to a 3-1 win over Greece.
"I'm not under more pressure because United are watching me, I'm glad that they do because that means I'm doing something good. It gives me more motivation to do better and better," he told Sport.ba.
"I'm pleased that the big clubs are interested in me, but as I said many times - I'm happy at Stoke City because the gave me a chance to play in the Premier League.
"We will see what will happen in the summer. In football you can never know what will happen."