Reports suggest Welbeck has grown tired of a lack of first-team football under Moyes and wants to leave Old Trafford.
Welbeck has scored 10 times in 32 United appearances this season, but he apparently has become frustrated at playing out on the wing.
The England international, who has two years remaining on his current contract, has scored six goals in six Premier League games when playing in attack.
When asked about Welbeck's future following United's 2-0 defeat at Everton on Sunday, Moyes said: "Danny Welbeck is really important to me and I really value him.
"There have been lots of stories. I can only tell you Danny Welbeck is really important to me and really important to Manchester United."
Welbeck, an academy graduate born in Manchester, came off the bench after 75 minutes at Goodison Park, but could not find the net as United stumbled to their latest defeat of a wretched season.