Virgil van Dijk claims he knows nothing of interest from English clubs and is keen to prove himself in the Champions League with Celtic.
QPR loanee Tom Carroll wants to "make it at Tottenham" but is prepared to consider all of his options at the end of the season.
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."