Stockton had his most impressive season with Morecambe last term, making 44 League One appearances and scoring 23 goals.
His displays have seen him draw the attention of a number of clubs including Port Vale, who want to improve their attacking department.
Morecambe were waiting for a suitable offer for the striker and have not yet received one to their liking.
Port Vale have now tabled a bid of £150,000 for the striker as they make an effort to snap him up towards the end of the window.
It remains to be seen what Morecambe’s response to their offer is and if Port Vale get their man this window.
Other than Port Vale, Fleetwood Town and Shrewsbury Town were also interested in him, but have now dropped out of the race.
Morecambe are said to be thinking of £600,000, in addition to bonuses for the striker, though Stockton himself is wanting to leave.