The Scottish Premiership champions are looking to strengthen their squad after reaching the group stages of the Champions League.
Manager Neil Lennon is understood to be keen to sign Holland Under-21 international Buttner for the rest of the season.
The left-back has failed to hold down a regular first-team role at Old Trafford since arriving from Vitesse Arnhem in 2012, making just 13 appearances.
Meanwhile, Tomlin has also reportedly attracted interest from a number of other clubs, including Crystal Palace and West Ham.
The 24-year-old is top scorer at Posh with six goals in League One this season, but the player is understood to be keen on plying his trade at a higher level.