Spurs boss Mourinho was reportedly unhappy with Southgate's treatment of the striker amid suggestions the 27-year-old is likely to start Wednesday's Nations League match against Denmark at Wembley (stream live on ESPN+ at 2:45 p.m. ET in U.S.).
However, Southgate sought to dampen rumours Mourinho had been in touch to express his concerns about Kane being asked to play while his fitness was an issue in his prematch news conference on Tuesday evening.
"I don't really understand the story because he's been fully fit since the end of last week, just before the last game," explained the England manager.
"He would have started the last game but hadn't had enough training time really. He was obviously fine during the game so he's fit, available.
"I didn't really understand the stories that were being run so where that's been coming from... it is certainly not the conversations we've been having with Spurs medically. And it is not something that is really affecting us in the camp.
"He hasn't had an injury. He was feeling muscle soreness which can happen to athletes but there was no injury at any point.
"We don't risk players. I've said this before the camp last week. I've been a player. My priority is always the welfare of players. We would never risk a player. We've ended up on very rare occasions with a couple of injuries during matches. That's pretty much unavoidable.
"But we've never lost a player through an error in terms of our training loading and we pride ourselves on looking after the players.
"We want them fit, we want them as sharp as possible for the games. Our issue with Harry before Sunday's game was to perform at the highest level. Now he's got an additional couple of days' training, it is not even an issue."
Southgate will be without Ben Chilwell and Kieran Trippier, however, after the former suffered a recurrence of a foot problem and the latter left the camp at St George's Park to resolve what the Football Association described as a "personal issue."
However, it later emerged Trippier is due to attend a hearing over an alleged breach of betting rules dating back to his move from Tottenham to Atletico Madrid in 2019.
Trippier has insisted he did not place bets or receive any profit from bets staked by anyone else. However, it is alleged he may have passed inside information to friends in a WhatsApp group, an act that would contravene FA rules and potentially lead to a worldwide ban for up to six months.
Sources have told ESPN the hearing has been scheduled for this week in part because Trippier was already in the country to represent England.