The Red Devils won their first Premier League game since 21 November on Saturday afternoon after a 2-1 victory over Swansea City at Old Trafford.
Louis van Gaal has appeared to temper growing speculation surrounding his position at United amid reports Pep Guardiola or Mourinho could replace the Dutchman.
However, former Red Devils striker Owen, who won the Premier League title in 2011, believes the axed Chelsea manager will replace Van Gaal at Old Trafford.
“They’re quite similar teams,” Owen told BT Sport.
“They’re built on a DNA of attractive football. He’s got a big chance of going to Manchester United.
“It’s going to be Giggs or Mourinho next.”
The Red Devils edged into an early second-half lead thanks to Anthony Martial’s goal before Swansea midfielder Gylfi Sigurdsson levelled with 20 minutes remaining at Old Trafford.
However, under-fire United skipper Rooney netted a brilliant strike with just over 20 minutes to go to secure the Red Devils’s first win in nine games in all competitions.
The 20-time English champions make the trip to Newcastle United at St James’s Park in their next Premier League game on 12 January.
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