Solihull Moors have rejected bids from League Two side Grimsby Town for two of their players, top scorer Akwasi Asante and midfielder Jamey Osborne.
Grimsby, managed by former Moors boss Marcus Bignot, have made improved offers for both the two 24-year-olds.
But BBC Sport understands that the bids fell well below the Moors’ valuation.
Other English Football League clubs have expressed serious interest in Osborne, but the Moors are not actively looking to sell either player.
Both remain vital members of Liam McDonald’s squad, who rose up to 15th in the National League table, nine points clear of danger, after their two Yuletide home and away victories over Chester.
Former Hednesford Town man Osborne scored his fifth goal of the season in the 3-0 win at Bumpers Lane on New Year’s Day, on his first appearance in a month, while Asante started on the bench in both festive fixtures.
Bignot left Solihull on 7 November to take over at Grimsby, who are back up to 12th in League Two after seven points from a possible nine over Christmas.