The 22-year old gloveman emerged as the Fire's number one this season, making 28 appearances, and the club feel he would benefit greatly from training with the reigning English champions.
Fire goalkeeping coach Aron Hyde told MLssoccer.com that plans were in place to get Johnson over to Old Trafford.
"It would be a really good experience for him if we can get it all set up properly," Hyde said. "Being around those guys and being involved will be good for him. It would boost his confidence.
"We're trying to set it up where we're trying to get him somewhere else as well, another Premier League team," Hyde added. "It should be a nice environment because those guys are flying and they're in the middle of their season and getting ready for the Christmas period which is obviously the busiest period of the year in England. It'll be good experience for him."