The 25-year-old talisman has not played since injuring ankle ligaments in the first leg of Spurs’ Champions League quarterfinal win over Manchester City.
That game takes place in Madrid on June 1, just five days before England face Holland in their Nations League semifinal.
Kane was included in an initial 27-man squad for the tournament named by Southgate on Thursday, with the final group of 23 to be confirmed on May 27. Place bet on Live Matches 24/7
“Frankly, we will know a lot more about that if he is in Tottenham’s team,” he said of Kane’s current fitness level.
Asked if Kane needs to play in the Champions League final to be considered for international duty, Southgate replied: “Not necessarily, because they might take a view that (Lucas) Moura scored a hat-trick (in the semifinal) and Son (Heung-min) played well so they keep Harry as an impact player.
Southgate said he was prepared to make a special case for his captain.
“Where there are one or two others we need to know a lot more about in the next week, he is one I will make an exception for in that I will see how it goes in the final week,” he said.
Kane is one of nine players from Tottenham and Liverpool who could potentially be involved in the Champions League final and go on to link up with the England squad in Portugal for the Nations League.
Southgate admitted the all-English final presents a rare challenge.
“That’s a test of our management skills and our collective spirit as a team,” he told BBC Radio 5.
“It’s the biggest challenge of all to compete against each other, then leave that at the door and remember with England we are a team, we support each other.
“That’s been a massive strength for us over the last 18 months.”