I think it's wise to wait until the end of the season to make the call. Certainly would be pretty silly to offer him a contract now when he's clearly not going elsewhere for the moment. Assess at the end of the season and make a decision in my opinion.
Also just to give balance to that managerial record, the last norwegian trophy win was in 2013, the ManU reserves trophies were all 2008 - 2010, and he's since failed with Cardiff in the Premier League/Championship, and been sacked. So he's done some good, but he's also had setbacks, and hasn't won a trophy for 6 years. It might be that the ManU job is the perfect fit for him, but surely give it more time first.
The Cardiff thing gets a lot of mention but there is a significant difference in a Cardiff squad which simply werent good enough to stay up and a Man utd squad that were underperforming. On top of that lessons learned from being unsuccessful with Cardiff might actually have made him a better manager than his time with Cardiff. The Cardiff argument is not really an important point given his very clear improvement since then. I failed school C first time around decades ago but then ended up with two entirely different degrees. People are able to improve with experience and time. Maybe just maybe thats what we see here.