Alderweireld, 28, returned to action earlier this month after a three-month spell on the sidelines due to a hamstring injury but was left out of the Spurs squad that played out a 2-2 draw with Juventus in Turin last week.
Pochettino explained after the game that he did not want to jeopardise the centre-back's career by playing him too much and risking a recurrence of his muscle injury.
Alderweireld was restored to the Spurs line-up for the 2-2 draw against Rochdale in the fifth round of the FA Cup during the weekend.
"I have recently had a good conversation with Toby Alderweireld," Martinez was quoted as saying by the London Evening Standard.
"I'm happy that Spurs take their time and don't rush him back. But of course, Toby would have liked to have played against Juventus. His situation will need time."
Alderweireld's omission from the squad for the Juventus match sparked speculation that the Belgian could be on his way out of the club in the summer, with the likes of Chelsea, Manchester United and Real Madrid all reported to be monitoring his situation.
The centre-back's contract expires in the summer of 2019, but Spurs have the option of extending it by an additional 12 months. Talks over an extension are reported to have reached an impasse.
Martinez said interest from big clubs in a player of Alderweireld's quality is normal.
"Toby has become one of the most consistent defenders in the Premier League," he stated.
"It's normal that his situation draws a lot of attention, certainly when he's nearing the end of his contract. But I think that he'll end this season in top shape."
Spurs chairman Daniel Levy said last month that he was "100 per cent confident" that the likes of Harry Kane, Dele Alli and Alderweireld would still be Spurs players next season.