Liverpool goalkeeper Pepe Reina would welcome a return to Barcelona next summer.
Sheffield Wednesday chairman Milan Mandaric has confirmed Neil Warnock is on a five-man manager's shortlist.
The 31-year-old has signed a three-year deal at the KC Stadium as the Tigers continue to prepare for their return to the Premier League.
McGregor told Hull's website: "I'm really excited to be here and I'm happy that everything is done now.
"I can't wait to get started here. This is a great chance for me to play in the Premier League and I'm looking forward to the season ahead."