Dier's current deal expires at the end of next season and he has watched as Spurs teammates Mousa Dembele, Christian Eriksen and Jan Vertonghen run down their deals.
Mourinho revealed that Spurs chairman Daniel Levy wants to extend Dier's stay in north London and said the 26-year-old is happy to do so.
"My boss Mr. Levy tells me that he wants Eric to sign a new contact and Eric tells me that he's more than happy here, more than happy with his situation, especially now that he feels we have a certain idea for him and the deal," Mourinho said ahead of Thursday's visit to Sheffield United.
"And he tells me also that he wants very much to stay. So I hope that we can find an agreement because I'm trying to take the team in a certain direction and when I try to develop a player in the team it's because I'm waiting for a player to stay with us."
Dier is still awaiting the outcome of an FA charge of "improper and/or threatening" behaviour after he climbed into the stands to confront a supporter who had reportedly been insulting his brother following Tottenham's FA Cup defeat to Norwich in March.
The outcome of the FA's investigation has been delayed by a Metropolitan Police probe – which determined no wrong-doing from anyone involved – and the three-month suspension of football.
Mourinho claimed he expected Dier to avoid a ban because Arsenal's Matteo Guendouzi escaped punishment for appearing to grab Brighton striker Neal Maupay by the throat in the Gunners' 2-1 defeat on June 20.
"I think they made a decision when Guendouzi grabbed the other guy by his neck," Mourinho said. "The decision was made in that moment."
Asked if he therefore expected Dier to avoid punishment, he replied: "What do you want me to expect?"
Dier rotated between midfield and defence under former Spurs manager Mauricio Pochettino but said in early March that he sees his future at centre-half.
Mourinho has since used Dier at the heart of his back four and he has looked steady since the Premier League restart, despite conceding a penalty in the 1-1 draw with Manchester United.
Asked about his defence, which kept only a fourth clean sheet of the season against West Ham last time out, Mourinho said: "I'm very happy. Of course the defensive organisation is not just about the keeper and the back three or back four.
"It's about the team and again, even speaking about the defensive organisation of my team I want to speak about my attacking players. The way they close spaces and respect organisation. The way they are learning to defend zonally.
So we are improving. I hope we are not saying this and then in the next two or three matches we concede a lot of goals. So hopefully the stats and the numbers are helping us, but our feeling is that we are improving, we are more stable and the team is getting better. That's why I'm saying independent of results and the table, I think when we start next pre-season we will be a better team than we are today."
Dier has been partnered by Davinson Sanchez since the restart but Mourinho added: "I'm happy with them but I believe that they are part of the structure and part of the organisation. I think if it's not them and it's Vertonghen or [Toby] Alderweireld, the thing would be the same.
"Good players, good structure, good understanding, less doubt. Better work by the zonal defending by the midfielders is very, very important for the team. So of course credit to Eric and to Davinson, but I truly believe that if it was Toby or Vertonghen the situation would be the same."