The Red Devils have been regularly linked with the English midfielder over the past couple of months.
Maddison has been one of the key players in Brendan Rodgers’ impressive Leicester side in the current campaign.
The 22-year-old has scored four goals and has made two assists in 12 games in the Premier League this term.
The Leicester playmaker was handed his England debut in their 7-0 victory over Montenegro in their Uefa 2020 qualifier.
Former Chelsea FC defender Burley believes Manchester United should consider a swoop to sign to Maddison.
“Of course they’d be interested in him and I believe they’re interested in him,” Burley told ESPN FC.
“Not before the end of the season because we don’t know what Leicester are going to do.
“It could be a great season for Leicester City, he’s a big part of that.
“United did want [Youri] Tielemans and Leicester managed to coax him into coming there.
“So you’re talking about trying to convince a guy who potentially is going to get an offer in the summer from Man United as I say.
“If they sold him in January, Brendan Rodgers might as well pack his bags and go.
“So I don’t think it will happen then but there’s potential for that to happen in the summer.”
Maddison has netted 11 times in 47 games in the Premier League over the past two seasons since his move to Leicester from Norwich City in a £20m deal in 2018.
The Red Devils have already raided Leicester City on one occasion this year after Manchester United signed Harry Maguire in a £80m deal from the Foxes in the summer.
In doing so, Manchester United made Maguire the most expensive defender in the world ahead of the Liverpool FC centre-half Virgil van Dijk.
The 20-time English champions have been linked with a host of English players since Ole Gunnar Solskjaer took over the reins from Jose Mourinho back in December.
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