Ings has one year remaining on his deal at St. Mary's and has recently rejected the offer of a new contract on the south coast. The proposed deal would have made him the best paid player in the history of the club.
The former Liverpool striker, who narrowly missed out on Gareth Southgate's England squad this summer, is keen to test himself at the highest level once more after injury blighted his time at Anfield.
Ings, 28, has scored 46 goals in 100 appearances since joining his boyhood club from Merseyside.
Tottenham striker Harry Kane is determined to leave the club this summer, with Premier League champions Manchester City his preferred destination, though Spurs chairman Daniel Levy is insistent the England captain, who is yet to meet his new manager, will not be sold.
Spurs have long struggled to find a partner or understudy to Kane but Santo is keen to add Ings to his squad and is thought to want to play with the pair as a front two.
Former Tottenham manager Jose Mourinho was interested in signing Ings last summer but failed to make a move materialise.