The 19-year-old featured in the 1-1 draw against Spurs in the FA Cup third round, and the Portuguese boss made a point of congratulating him on his performance once the players left the field.
Jose is a long-term admirer of Spence having kept tabs on the full-back since Fulham released him from their academy, and Tottenham are now tracking him as they are in the market for a right-back.
The teenager has only been identified as a possible future signing, though, and a move for him this month doesn’t appear to be on the cards.
Spence recently became a first-team regular at Boro, featuring in nine games thus far, and he has 18 months left on a youth-team contract.
The Championship side want to offer him a new five-year deal, and talks are ongoing.
Spurs are set to allow Kyle Walker-Peters join Crystal Palace on loan till the end of the season and could look to bring in a right-back.
They could also do with another striker and midfielder with Harry Kane and Moussa Sissoko both ruled out for some months.