According to The Sun's Mike McGrath, Guardiola is hoping to bring in a world-class defender to succeed the injury-prone Kompany and has identified the player's compatriot, who is valued at £60 million.
Speculation has been rife over the 28-year-old's future since his adviser, Stijn Francis, told Nieuwsblad (h/t ESPN FC's Dan Kilpatrick): "He deserves either a correct contract from Tottenham or a transfer."
According to Alex Young of the Evening Standard, Alderweireld earns a relatively low £50,000 per week.
Squawka's Connor Humm is surprised more hasn't been made of the Belgian's contract situation given his status in the Premier League:
Connor Humm @TikiTakaConnor
All the spot light on Özil and Alexis but the leagues best centre-back at Spurs is in the same situation. Alderweireld still hasn't signed.2017-9-4 11:18:08
Young reported the defender's deal runs out in 2019 with the option to extend by another year, so his situation isn't nearly as urgent as those of Arsenal's Mesut Ozil or Alexis Sanchez, whose contracts expire at the end of the 2017-18 season.
Tottenham boss Mauricio Pochettino has played down talk of him leaving, per Young: "He wants to make it clear he is fully committed with the club. He's happy with his contract, two years plus one. It's not an issue."
Nevertheless, tying him down is still crucial to Spurs' success in the coming years.
Alderweireld is an outstanding centre-back and has played a significant part in Tottenham boasting the best defensive record in the Premier League over the last two seasons.
City have great need for a player of his calibre at the back. Even during Saturday's 5-0 win over Liverpool, they showed their defensive frailty without Kompany as the Reds repeatedly gave their back three a torrid time, with the Reds let down only by their own poor finishing.
He suits Guardiola's style, too. Yahoo Sport's Ben Pearce provided an example of the way he plays the ball out from the back:
Ben Pearce @BenPearceSpurs
#thfc 15' Another good move. Alderweireld through to Eriksen, who frees Davies. He cuts ball back to Sissoko, who's free & sees shot blocked2017-9-9 14:15:39
As Squawka Football demonstrated, the defender is successful at it:
Squawka Football @Squawka
Toby Alderweireld has completed more long balls (36) than any other player in the Premier League this season. Goalkeepers included. 🎯 https://t.co/qTVGTaEIwn2017-9-10 21:51:00
He'd be a magnificent acquisition for City or virtually any side in world football, such is his level, and the Sky Blues could offer much more lucrative terms than those he's currently on.
His contract situation may not yet be desperate, but if he still hasn't signed a new deal by next summer, clubs like City will most likely be ready to make a move for him.