The 28-year-old was the subject of yet more weekend speculation linking him with a move away from the Mazuma Stadium.
The rumours come after a season during which he scored 26 goals in 50 outings across all competitions.
Twenty-three of those came in League One as the Shrimps finished two points clear of the relegation zone, seeing him finish as the division’s joint-third highest scorer.
Adams’ predecessor, Stephen Robinson, had said three months ago that he wanted to offer the striker new terms.
Speaking on Monday morning, Adams reiterated the club’s desire to retain a player who still has 12 months left on the two-year contract he signed last summer.
The manager said: “We haven’t had any interest in Cole Stockton, we’ve had no dialogue with any club at this moment in time.
“We are in the process of making Cole the highest paid player at the club and we are in the process of offering him a new contract: an extended contract.
“We have set our stall out in terms of what we want to do. He has got another year to run on his contract and we would like to extend that.”
Having rejoined the Shrimps in the summer of 2019, Stockton has blossomed in the last two seasons.
The quantity – and quality – of Stockton’s goals in the 2021/22 season, coming for a team finishing just above the bottom four, was always going to trigger speculation of interest from elsewhere.
However, while acknowledging that inevitability, Adams warned would-be suitors that Stockton would not leave on the cheap.
“That’s always going to be the case,” the manager said of transfer rumours concerning his striker.
“The owners have a value on the player, as they have on all the players at the club.
“If someone comes in and offers that money, then they want to be recompensed in the way that they were with Sam (Lavelle) and Carlos (Mendes Gomes) last year.
“They will, however, be looking for more money than they got for both of those players.”