Rojo was missed as United dropped points in their Premier League clash with Stoke City on Saturday (21 January), needing Wayne Rooney to rescue a point for his side with a last-minute free kick – his record-breaking 250th strike for the club.
United revealed before of kick-off that afternoon their Argentine international was sidelined due to illness. But speaking to the press ahead of his side's visit to the KCOM Stadium on Thursday, Mourinho revealed he now has a fully-fit squad to choose from.
The squad will also soon be bolstered by the return of Bailly, who has become an instant fan favourite after an impressive first-half of the 2016-17 season. The 22-year-old was named in Ivory Coast's squad for the African Cup of Nations, leaving United with the possibility of being without their centre-half for 10 matches, had The Elephants reached February's final.
Their elimination at the group stages of the competition on Tuesday however means the former Villarreal defender will soon be on his way back to Manchester. While Thursday's meeting with Hull will come too soon, Mourinho says there are "no problems" with his imminent return.
"Everybody is available," Mourinho told MUTV. "Bailly didn't arrive yet but his national team had a defeat yesterday and are knocked out of the competition, so he is coming back. In this moment everybody is available and my choices will be to try to go with a team that I think can guarantee us a good match."
Luke Shaw is also available to make his return. The England international has not featured since United's 4-1 win over West Ham United in November and has been working his way back towards full fitness, with illness preventing him from returning in the recent FA Cup third-round meeting with Reading.