Executive vice-chairman Ed Woodward insists Manchester United are ready and willing to break the British transfer record.
Newell's Old Boys are confident they can end Ignacio Scocco's Sunderland struggles and take him back to Argentina.
The 25-year-old Hungary international joined Wanderers in the summer of 2007, moving from boyhood club Vasas SC.
Following a single appearance during a loan spell with Crewe two years later, Bogdan made his Bolton debut in the August 2010 League Cup trip to Southampton and went on to play nine games in all competitions that season.
At the turn of this year an injury to Jussi Jaaskelainen offered him another first-team chance and Bogdan went on to dislodge the long-serving veteran as Bolton's No.1, a position he retained this season despite Andy Lonergan's arrival from Leeds.
"I'm delighted with the extension," he told the club's official website. "I think it's always a good feeling when the club wants to extend.
"I hope it's a good message for everyone and proves that I see my future here and that I am enjoying playing for the manager. I want to get back to the Premier League as quickly as possible and I see this as a big step."