Mourinho wanted his vice captain to get enough rest due to Tottenham’s busy start to the 2020-2021 season.
Kane has been playing through a thigh injury and needs to undergo a scan.
The 27-year-old came on as a substitute midway through the Three Lions’ 2-1 victory over Belgium on Sunday.
Mourinho is reportedly unhappy as he fears Kane could aggravate his injury if he plays against Denmark on Wednesday.
Southgate was asked in his press conference if he has been approached by Tottenham in regards to Kane.
“Well, medically, there’s been conversations, because that would always be the case,” the English coach told reporters.
“He reported on Sunday, we gave players that reported on Sunday, who weren’t involved in the Wales game for us, we gave them two days’ recovery.
“He started to train on Wednesday, was a little unhappy with how he felt, so then worked with our medical team the next couple of days, we scanned just to be certain but it’s a muscular fatigue issue rather than an injury, so it just needed a bit more confidence.
“He knew by then he could push on a little bit, but he just needed a bit more confidence in it, and so his training week really wasn’t suitable to start the game.
“I think he’ll have gained more confidence from the spell he had against Belgium, and so all being well, we hope he’ll be good to start on Wednesday.”
