Former Bulgarian international Berbatov was expected to move to Fiorentina but the Serie A team said he failed to turn up for a scheduled meeting in Italy on Wednesday.
"Berbatov is finishing his medical and if everything is good he will be one of our players," coach Martin Jol told the club's website.
"There were a lot of clubs interested but we were able and capable of getting him. He was on my list all the time - I tried to do something months ago and it didn't come off so I came back and it was the right moment for him to make his decision."
Berbatov played under Jol when the Dutchman was in charge of Tottenham Hotspur. The forward left White Hart Lane for Old Trafford in 2008.
The 31-year-old struggled to hold down a place in the United first team last season and seemed set for a move to Fiorentina.
"The player embarked in the company of his agent and with tickets paid by Fiorentina on a direct flight to Florence," the Italian club said. "But the player never arrived."
Jol also said a fee had been agreed for former England international Richardson.
"We are talking to Richardson and hopefully he will come to us," the Dutchman explained. "I see him playing as a winger."
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