As per Record, the 24-year-old is valued at around £30m and the Londoners are reluctant to pay that much for Grimaldo.
Jose Mourinho needs to improve his left-back options and Grimaldo could prove to be a quality addition. He has proven himself in the Portuguese league and in the European competitions.
Grimaldo has the ability to make the step up to the Premier League.
Spurs currently have Ben Davies and Danny Rose as their left-backs. Rose is on loan at Newcastle and he is expected to leave permanently this summer.