After netting 18 goals in all competitions last season, a host of teams are believed to be keen on Cook who has 12 months remaining on his deal at the Banks’s Stadium.
The Express & Star understands League Two rivals Salford City and Grimsby are among the clubs interested in the 28-year-old.
Clarke is currently at the start of major rebuilding job, with the Saddlers currently having just 13 first-team players on their books.
And the boss says he is focused on building his squad rather than seeing key players leave.
“There will always be interest in players that score goals up and down the country,” Clarke said.
“For me, Andy is a Walsall player and I will crack on with the squad that I have got here.
“I want to build on the squad I have got.
“Different scenarios unfold during the course of the season and through the course of the window and we will look at everything.
“But for me, Andy Cook is a Walsall player and he will continue to be a Walsall player unless it is right for the club.”
Clarke has now been Saddlers boss for almost a month having been appointed on May 10.
And he admits the job is keeping him busy.
“It has been busy,” he continued.
“My phone has constantly been attached to my ear speaking to people and trying to get things sorted out and organising things.
“It’s pretty much what every football manager up and down the country will be doing.
“Albeit I have started a little bit early and maybe some of them are on their holidays, but no it has been good to get cracking.”
Meanwhile, Walsall have announced they will play Villa in a pre-season friendly on Wednesday, July 24.
The match, which will see former boss Dean Smith return to the Banks’s Stadium, is likely to be the only friendly the Saddlers play on home turf this summer.