The January window closes at 11pm on Monday with the Shrimps’ striker the subject of speculation across various transfer sites.
Stockton is League One’s second top scorer with 17 goals and 20 for the season, an invaluable contribution as the club aims to defy those pundits who tipped them for relegation before a ball was kicked this season.
O’Carroll said: “Speaking for myself and the staff, we don’t want Cole to go anywhere.
“He’s been fantastic, he’s been the leader of the team and while his goals have been brilliant, his overall play is fantastic as well.
“There’s always going to be interest but he’s a massive part of what we want to do and we’re planning to be with him going forward.”
Morecambe have had two busy windows since Robinson’s arrival last summer in the wake of Derek Adams’ departure.
Nineteen players were brought in as he put together a new squad, almost from scratch.
This month has been less hectic in comparison, though there have still been loan moves for Trevor Carson and Jacob Bedeau, as well as the short-term signing of Ousmane Fane.
Those have been offset by the departures of loanees Jokull Andresson, Josh McPake and Callum Jones, along with permanent exits for Scott Wootton and Shayon Harrison.
Nevertheless, O’Carroll anticipates there may be further business to be done at the Mazuma Stadium.
“The window is a stressful time for everyone whether that’s incomings or outgoings,” he said.
“You’re always going to have a bit of movement. Even if you were at a club that’s 10th in the league, you would always think there might be a couple out and a couple in.
“We knew in the summer that we would need to add to the group.
“I do envisage we will be busy for the next couple of days, whether that be boys coming in or going out.”
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