Tottenham want Ings, but Southampton don't look favourably on his sale, so the board are working to improve his contract. 'The Athletic' assure that that is the club's intention, as the player is currently one of the most important in the team.
Proof of it is in his numbers from last season. He scored 25 goals, the second-highest in his whole career, in 42 matches of which he started 35. He is maintaining his high performance at the start of the current season, which keeps Spurs in the hunt to sign him.
The most likely scenario is that, if his side reach a deal to extend his contract, his salary increases so that he is happy. Perhaps the negotiations include a high release clause so that Spurs have it even more difficult.
Tottenham already made a formal offer that Southampton rejected. It wasn't leaked how much money was put on the table for him, but his market value, facilitated by the parameters of profootball, allows you to get an idea. It is valued at around 24 million euros.