The Swedish striker worked with Mourinho during the 2008/09 campaign at Inter Milan as the Nerazzurri claimed the Scudetto.
Ibrahimovic opted to leave Paris Saint-Germain at the end of last season when his contract came to an end and decided to link up with Mourinho at Old Trafford.
The 35-year-old says he could have joined United the previous summer when Louis van Gaal was in charge but he wanted to see out his deal at the Parc des Princes.
The former Barcelona striker was linked with a host of clubs during the transfer window but he says Mourinho convinced him to make the move to Manchester.
"There were talks about me coming to United one year ago, that is correct. But I didn't believe in it then because it was not the right moment," he said.
"Then they get the Special One and, when the Special One calls you and when he starts to talk to you, you are already convinced. He didn't need to talk a lot to convince me.
"It was only enough to call me and say, 'Listen, I'm waiting for you in Manchester,' and I was coming."
United face a Premier League trip to Liverpool on Monday evening and punters may wish to use their free bet to back Ibrahimovic to open the scoring at Anfield.