Jose Mourinho wants Jan Vertonghen and Christian Eriksen to follow Toby Alderweireld in committing their futures to Tottenham.
Vertonghen and Eriksen both see their current contracts expire at the end of the season and Eriksen, in particular, had been hoping to leave the club in the summer.
Alderweireld put to bed more than 18 months of speculation over his future by signing a new three-year extension on Friday.
Speaking exclusively to Sky Sports in an in-depth interview you can see more of from 1pm on Super Sunday, Mourinho said he thought both Vertonghen and Eriksen should sign new deals to be part of the next step in the club's future after both playing an important role in Spurs' recent history.
"If I was Jan or Christian, I would stay," Mourinho told Sky Sports.
"Because they have been here for such a long time, they are living the life of the club in the past four, five years, the transition to White Hart Lane to the best stadium in the world, the perspectives of the future, the vision of the club, if I was them I would say I want to be part of the next thing."
Speaking ahead of Spurs' clash with his former club Chelsea, Mourinho told reporters: "I would like Jan to sign a new contract. [And] the only thing I will say about Christian is that I want him to sign a new contract. Apart from that I won't say anything else [about him].
"I think a player will sign a contract when the club wants - I am the club, Mr Levy is the club - when the player wants, when the family wants, when the agent wants. If one of these parts doesn't want it is very difficult to happen, unless the player changes agent and gets one that also wants [it].
"The most important thing is what Toby said. 'I couldn't be happier anywhere else'. That is fantastic."
On Alderweireld's new contract, Mourinho told Sky Sports: "When I arrived, we had three top players potentially leaving, now we have two top players potentially leaving. It's going to be two, one or zero. I can't tell you.
"I'm very happy that it's not three, yesterday it was three and this morning it's only two. I don't think it's my influence with Toby, there's a good feeling between us and maybe that helps a little bit, but from the negotiation point of view it's nothing to do with me.
"I read some quote from him saying there's no place where he can be happier than this and that's the biggest reason he's staying, because he could get a better contract somewhere else. It helps that since I've arrived he's played every minute of every game, probably. He probably feels like he's going to play under me, he's going to be first choice, and maybe that helps.
"I don't want to share much, but my situation with Toby was from the beginning a clear desire of everybody to commit and get a new contract. When I say everybody, it's not just sometimes about the club and the player, there's other parties involved, and it's important they don't think in a selfish way but what the player would like. It was very important."
Mourinho avoided being drawn into critiquing his former club Chelsea and their manager Frank Lampard, who played under Mourinho for trophy-laden seasons until 2007.
Mourinho: I'm 100 per cent Tottenham
Jose Mourinho says he is now "100 per cent Tottenham" ahead of facing his former club Chelsea in Sunday's London derby and claims he has "no space for previous clubs".
But he said they should not be underestimated just because they have embraced playing several academy graduates with little Premier League experience.
"To call Antonio Rudiger, Marcos Alonso, Cesar Azpilicueta naive is hard," he said. To say they have a couple of young players without experience is the same thing I say about players like Troy Parrott, or Scott McTominay or Marcus Rashford.
"There is always a beginning [for a player]. And I think [the Chelsea players] they are doing very well."
Watch the full version of "The Mourinho Effect" after Super Sunday on Sky Sports Premier League at 7.30pm on Sunday.