Alderweireld rejected a move to Norwich City earlier in the summer after failing to agree personal terms regarding a switch to Carrow Road.
Liverpool have long been linked with a bid for the 24-year-old, while reports on Sunday claimed that Tottenham have joined the chase for Alderweireld.
The speculation suggested that Spurs boss Andre Villas-Boas wants to sign Alderweireld and his Ajax team-mate Christian Eriksen in a £15million double deal.
However, according to the Dutch media, Russian outfit Spartak Moscow are the club to have submitted the latest offer for the defender.
Ajax's director of football Marc Overmars declined to name the interested party, but confirmed talks are ongoing.
"We have received an offer," Overmars told De Telegraaf. "We won't give any names as we are still in talks.
"But, just like with Norwich City earlier, I expect we can work out a deal with this club."
Alderweireld has one year left on his contract at Ajax and has previously expressed a desire to move to either the Premier League or Bundesliga.