Irwin believes the Red Devils must inquire about the England international if there is a possibility of securing his services.
Kane has put a lot of big European clubs on alert after it was reported that the 27-year-old is searching for a new club, who can meet his ambition.
The 27-year-old’s future has been uncertain for quite sometime now and reports have revealed that Kane had talks with club chairman Daniel Levy on Monday, and has made his intention of leaving known to the board.
Speaking to BBC Radio, the former Manchester United man says Ole Gunnar Solskjaer must take a look at Kane’s current situation in North London.
“If any players of that quality come up you’ve got to be in the market and find out whether he wants to come," Irwin said.
"Great that Edinson Cavani has signed for another year, and what Marcus Rashford, Mason Greenwood and Anthony Martial can learn from but if Harry Kane comes on the market a club like [United] has got to look at that option.
"He’s a scorer of goals, a fantastic goalscorer, knows the Premier League inside out. It can’t be easy for him because Spurs are his boyhood team, it’s always more difficult when you want to leave, but he’s at the age now he wants to challenge for trophies, so that’s showing ambition.
"He’s given great time to Spurs but if someone of that quality comes on the market you’ve got to look at it."
