But while a number of teams in League One and League Two are believed to be keen on the 28-year-old, the Saddlers are yet to receive a firm bid for the frontman.
Cook moved to the Banks’s Stadium on a free transfer last summer and finished the campaign as Walsall’s top scorer after netting 18 goals in all competitions.
That form has alerted other clubs, with Cook having previously scored 51 times in 89 appearances for Tranmere.
But while Cook has plenty of admirers, it is understood Walsall would not welcome any offers with the club hoping the forward can play a key role in a promotion push from League Two.
Cook, who is from County Durham, enjoyed two years with Grimsby between 2012 and 2014.
And it is understood Mariners’ boss Michael Jolley is eager to land a striker who can take his team to the next level.
Grimsby finished 17th in League Two last season with striker Wes Thomas – who scored 11 goals – the only player to hit double figures.
And the Mariners believe Cook is the man to fire them up the table.
Salford meanwhile are expected to renew their interest after the forward turned them down to join the Saddlers last summer.
The club, which is owned by Manchester United’s class of ‘92 as well as billionaire Peter Lim, offered Cook more money to move to Moor Lane.
But the forward rejected the offer because he was eager to prove himself in League One.
After winning the National League play-offs though – and following Walsall’s relegation – the two teams will both be in League Two next year.
And Salford have the financial clout to test the reserve of both Walsall and Cook if they decide to make a bid.
Cook has also been linked with former club Tranmere as a replacement for James Norwood who is expected to join Ipswich.