They had previously been demanding €40m (£37m) for the Poland international, a fee Spurs were not willing to match, though they have now reduced that to €25m (£23.1m).
This decision comes after Roma came in with an offer of €15m (£13.9m) plus a couple of youth players in an effort to sign the 26-year-old, who scored 14 goals across all competitions for Napoli last term.
Spurs are looking to sign a frontman who can act as back-up to the talismanic Harry Kane, and it is claimed they have already sent an offer to Milik’s entourage in the hope it will help to bring about a move.
The offer is said to relate to wages, which could see the former Ajax man sign a pre-contract agreement and join next season, when his contract comes to an end.
However, Napoli want to get rid of Milik, the player is keen to leave and Jose Mourinho feels he needs another striker as soon as possible, so it is likely that work will be done to make the move come about sooner.
As things stand, Spurs don’t have a single recognised senior striker to fill in if anything were to happen to Kane.