Roma announced this week that Mourinho, who was sacked by Tottenham last month, would take over from Paulo Fonseca at the end of the season.
Mourinho previously coached in Serie A between 2008 and 2010, winning the treble with Inter.
The Italian club this week sealed their first league title since the Portuguese’s triumph, with Conte at the helm.
Conte and Mourinho butted heads in 2018 while the Italian was Chelsea boss and Mourinho was at United, but Alessio has said the tension between the pair is not as great as many fans believed.
“They are a bit similar; they have strong characters and maybe that can be one of the reasons why they clashed,” Alessio, who also assisted Conte at Chelsea, told Football Italia.
“I remember we beat Manchester United in 2018 and Mourinho was upset due to Antonio’s celebration. They continued to taunt each other for some time after that.
“Sometimes things get blown out of proportion. There were not pleasant words between them, but it all began with a misunderstanding.
“That time, Mourinho was annoyed with Conte’s celebration, but that’s what Antonio always does – everyone knows that. It was a regular celebration for him.
“They are smart people, so in the end they cleared the air. Now they respect each other and I am sure we’ll see that when they meet next season.”
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