The talks come after Keane Lewis-Potter moved to Brentford for £16million which will have no doubt prompted Hull to turn their attentions to their other young star.
Greaves has been attracting interest from watching eyes which is prompting the Tigers to strike up an agreement with the youngster who played every minute last season.
Hull vice-chairman Tan Kesler has been speaking to media about conversations with Greaves, revealing them to be positive, telling the Hull Daily Mail: “Jacob and I had a conversation, I think we’re at a very good stage, a very, very good stage.
“All credit to Jacob, now he sees me and he sees Acun, we’re present, we’re talking to him and we’re trying to understand him and we’re getting to know each other.”
Kesler has been spending time with the team while they’ve been out in Turkey and Spain as part of their preseason tour, spending time on the golf course together as the new season approaches.
This gave Kesler the opportunity to have a very open conversation with the young star, and he added: “I promised him, I said to him that he’s a young man with tremendous potential who is making his legacy here.
“But he needs another year to establish that legacy and if he wants to leave, then it’s too early, in my opinion, I told him this very openly.
“We’re going to come to the table with his family and representation and I think we’ll achieve it, you know because he’s a good guy. We need him as the next Hull figurehead.”
To date, Greaves has made 89 first-team appearances in all competitions for Hull after coming through the club’s academy, scoring once in that time.
It’s a very frank and open discussion to have between the two and if the outcome is a new deal for Greaves, then it will have been a success.
But seeing Lewis-Potter leave for a Premier League club, this may make Greaves think that the next opportunity is one that he’ll need to snap up.
That being said, this was Greaves’ first full season of Championship that came with plenty of learning curves and at 21, there’s still time for him to develop as a defender at this level.