The Championship club recently turned down a £12million bid from Burnley for last season's top scorer Chris Wood but have expressed a desire to bring in Lasogga in order to strengthen their attack and increase competition for Wood, and recent signing Caleb Ekuban.
Immediate rumours were that the offer must have come from Burnley, given their desperate need for a new striker after the sale of Andre Gray to Watford, and the fact they have had a £12m offer already rejected.
United won their opening Championship fixture 3-2 away to Bolton Wanderers before drawing 0-0 with Preston North End on Saturday.
United are confident a deal can be struck to sign Lasogga, who they have been monitoring for some time, as they prepare for an improved Burnley bid for 27-goal man Wood. But if we want to achieve something this season, you can not sell your best players.
It was his nose for goal that has seen him monitored by other Premier League outfits, such as Southampton, Swansea City, Brighton and Hove Albion, and Stoke.
Wood, who showed flashes of the talent that has piqued the EPL clubs' interest, came close to scoring in the final stages but was foiled by an excellent save by PNE keeper Chris Maxwell, who kept his club in the hunt with a string of important interventions.