Reports have suggested that Manchester United have previously been put off by Spurs' valuation of the Belgium international, which is said to be in the region of £75m.
However, according to Yahoo! Sport, Spurs have suggested that they are willing to further discuss an exit for the 29-year-old, who has spent the last month representing his country at the World Cup.
The North London outfit are aware that a clause in Alderweireld's contract will allow him to leave for £25m next summer, leaving open the possibility of a sale for a bigger fee in the coming weeks.
United boss Jose Mourinho is allegedly keen to strengthen at centre-back before the start of the new season.