The Ajax star has previously been linked with a move to Norwich this summer but, with that move scrapped, he is now set to decide on his next club
The 24-year-old Belgium international, who can play at both centre-back and right-back, was linked with a move to Norwich earlier this summer until his representative revealed he failed to agree personal terms with the Canaries.
But Soren Lerby has now claimed Everton have entered the race for Alderweireld's signature, but face competition for his client.
"It's true that Everton have made an approach for Alderweireld," Soren Lerby told Gazet van Antwerpen.
"But there are other concrete options. Toby will now have to decide which team he sees as the biggest challenge."
Alderweireld's contract expires next summer and has been previously linked with moves to Liverpool and Tottenham, while Ajax signed potential replacement centre-back Mike van der Hoorn in July.
Everton manager Roberto Martinez has been busy in the transfer window so far, adding centre-back Antolin Alcaraz, goalkeeper Joel Robles, forward Arouna Kone and Barcelona’s on-loan attacker Gerard Deulofeu to his squad.