The Colombia international has been in impressive form for Roberto Mancini’s Inter Milan side so far this season.
Murillo has scored two goals in 27 Serie A appearances for the Italian giants so far this season.
The defender has experience at international level after racking up 16 appearances for the Colombia national team.
According to the Daily Mirror, Inter have placed a £23m price tag on the Colombian’s ahead of this summer’s transfer window.
United have a poor record with Colombian players after Radamel Falcao disappointed during a season-long loan in 2014/15.
The former Atletico Madrid and Porto striker scored just four times in 26 Premier League games for the Red Devils.
Louis van Gaal has used Netherlands international Daley Blind as a makeshift centre-half for most of the season.
MORE: The latest football news