Maguire finally completed an £80m move from Leicester City to Old Trafford on Monday, bringing to an end a long period of protracted negotiations.
Maguire’s transfer fee surpassed the £75m Liverpool paid Southampton to price Virgil van Dijk from the Saint Mary’s stadium in January 2018.
Van Dijk coped admirably well with the tag as the costliest defender, helping Liverpool to within inches of the Premier League title last season before marshalling the Reds defence to a sixth European crown in June.
Maguire faces a tough task of helping Manchester United reclaim its place among Europe’s elite after last season’s disappointing sixth place finish, and Van Dijk has sent a word of caution to his rival regarding his price tag.
“Good luck to him,” the Liverpool defender told reporters.
“I can’t say anything about that because there was always going to be a time when it was going to change. That’s the market. He doesn’t have any influence on that but I wish him well.”
“The price comes with pressure but it doesn’t change too much because you always have pressure at big clubs like Man United. But I wish him well.”
“It is not easy to completely shut off all the pressure. Personally, I like to put things in perspective,” Van Dijk added.
“Quite a lot of things are more important than playing football and what we do, we are blessed
“Just focus on doing what you love to do and play your best game. Get your qualities out of the pitch, enjoy your game and don’t think about the other things.”
Maguire will be available to make his debut for United in their Premier League opener against Chelsea at Old Trafford on Sunday.