José Mourinho expects Harry Kane to play only two Premier League games before Euro 2020. The Tottenham manager has been without Kane since New Year’s Day, when the striker ruptured a hamstring tendon in the defeat at Southampton, and has previously raised the prospect of him missing the rest of the season.

Mourinho said on 13 January that the England captain would be “out until mid-April, end of April, May, next season, I don’t know” – a comment that reflected the level of concern he had, even if it was undercut by vagueness. As the manager prepared for Wednesday night’s FA Cup replay at home to Southampton, he was more specific.

“The Leicester match,” he said when asked about Kane’s return. Spurs face Leicester at home on the weekend of 9-10 May before playing their final game of the league season at Crystal Palace on 17 May. “Maybe we need that match for something. To be fourth, to be fifth, to be sixth. Maybe he can help us in this match. I hope. Is that the best-case scenario at the moment? Yes, I think so.”

Spurs have indicated that Kane should return to action in mid-April but Mourinho has consistently painted the gloomiest picture, which is a worry for both the club and England. The national team face Croatia at Wembley on 14 June in their Euro 2020 opener and before that they have warm-up fixtures away to Austria on 2 June and at home to Romania on 7 June.

There has long been concern at the Football Association that Kane will be the latest key England player to face a race against time to recover in time for a major championship, a list that is headlined by David Beckham and Wayne Rooney, although Mourinho cares little about that. “It’s a problem for [Gareth] Southgate and for [the England assistant manager] Steve Holland, not for me,” he said. “How would I feel if I were England manager? I don’t know. I’m not.”

What concerns Mourinho is how Spurs will cope not only without Kane but in the absence of any recognised senior No 9 for the majority of the season. Mourinho has always relied on a targetman and he was unhappy at the club’s failure to sign a back-up in January.

Spurs did get the winger Steven Bergwijn and the midfielder Gedson Fernandes which, to the manager’s mind, offset the departure of the playmaker Christian Eriksen. But he suggested that when the long-term injuries to the midfielder Moussa Sissoko and Kane were factored in, the squad is weaker now than when it entered January.

“We found our balance [in midfield],” Mourinho said. “Without injuries, I would say: ‘Yes, good.’ But we had these problems with important injuries and of course our squad in this moment is not as good as it can be. When our injured players are back for the next season, of course the squad will be much better.”

Mourinho may have an ulterior motive for being cautious about the comeback of Kane, who posted a video last week of him working in the gym to stretch the hamstring with a resistance band. The manager does not want to put undue pressure on the player during his rehabilitation.

“With [Hugo] Lloris, we were speaking about February [for him to return from elbow surgery] and he came back in January,” Mourinho said. “It’s better not to put any kind of expectations, any kind of pressure. Let it go and let’s see. There has not been a setback [for Kane]. Nothing has happened. Everything is OK. He’s having his treatment.”

Mourinho thinks Dele Alli has a chance of playing against Southampton after escaping serious injury in Sunday’s win over Manchester City, when he was caught by a late tackle from Raheem Sterling. “It’s not as bad [as feared],” he said. “Dele was very lucky.”