Ighalo joined United on transfer deadline day, making the move from Chinese outfit Shanghia Shenhua on a six-month loan.
It comes with Ole Gunnar Solskjaer having been desperate to sign a striker following the departure of Romelu Lukaku in the summer.
Lukaku headed to Inter Milan having struggled at Old Trafford with Solskjaer unable to replace him in the previous transfer window.
And, having signed former Watford striker Ighalo, Burley believes that Lukaku will see the funny side.
“I saw [Ighalo] play quite a bit for Watford and he did a decent job for them, but this is Man United we’re talking about,” Burley said on ESPN FC.
“I get that they need to get a player in, however when you go from one of the best talents in European football in Erling Haaland, to Edinson Cavani one of the best talents of the last decade, to Josh King at Bournemouth and now to Ighalo playing in China, Romelu Lukaku must be sitting with his feet up in Milan, chuckling away like never before.
“He might score some goals and that will be what he’s brought in for clearly, he might get some goals for them.
“But however, it’s Man United we’re talking about, someone who previously went out and got Henrik Larsson in January. Good grief.
“Man United are still chasing the top four, right, it’s viable.
“They’re in the FA Cup still, they’re in the Europa League still, they’ve got quite a bit to fight for as bad as they’ve been.
“Another point on this [no option to] buy thing, who gives a damn? He’s 30 years old, that goes against the grain of what they’re going to do anyway, so they aren’t buying him at the end of the year.
“But I go back to the point - it’s Man United we’re talking about.
Ighalo is set to head to United from China this weekend and could make his Red Devils debut against Chelsea on February 17.