Alderweireld is out of contract at the end of next season and a clause in his deal means he can leave in the summer for only £25million.
And The Sun say that has alerted Arsenal whose season has been marred with a host of injuries to their backline.
It is claimed no official approach has been made but that Arsenal are monitoring his situation and would like to get him because he would be cheaper than some of their other targets.
If Unai Emery’s side do not qualify for the Champions League next season, the manager could be left with a budget of only £40m to rebuild a squad that requires major surgery.
At £25m, anybody who does sign Alderweireld, 30, would be getting him at way below his market value.
Manchester United are also understood to be interested and were quoted £60m when former manager Jose Mourinho tried to him last summer.
The Belgian will not be short of suitors if he does leave Spurs, with Chelsea and Manchester City both reportedly keen as well.
Alderweireld moved to Spurs from Atletico Madrid in 2015 after a successful loan spell with Southampton.
He has made 155 appearances in all competitions and scored six goals.
If he does move to Arsenal, he would follow in the footsteps of Sol Campbell who made the same switch to Spurs’ north London rivals in a bitter transfer.
Campbell ran down his contract at Tottenham before moving to the Gunners on a free in 2001 and went on to win two Premier League titles, going the entire season unbeaten in their 2003-04 ‘invincibles’ campaign.
Former Gunners striker Alan Smith believes he would be a superb signing for any team in the Premier League.
“For someone of his ability and experience, £25m is a pittance,” he told the Evening Standard.
“No wonder top clubs have been linked with a summer swoop for the Belgian. So what do Spurs do?
“Try to persuade him to stay with a new deal or let him go, possibly to a direct rival?
“Alternatively, bank on the likes of the unproven Juan Foyth filling the gap? It’s a key decision on which Mauricio Pochettino will doubtless have a say.”