Lester will end a six-year association with the club following the final npower League Two fixture of the campaign against Exeter at the Proact Stadium on April 27.
Cook said: "He is a proper club legend. There's not many of them about, but Jack certainly is one.
"What I'd like to do at the moment is let Jack get his messages out and be treated with the utmost respect, which he deserves.
"Jack has only just made the announcement so I'd like to show him a little bit of respect and let that be channelled properly before we pay our respects, and there will be plenty of them.
"I think when people go through football clubs like Jack Lester has gone through ours, they deserve all the plaudits and recognition that will come over the next month or so and I'll certainly be leading those choruses and echoing everyone else's sentiments."
Lester joined Chesterfield from Nottingham Forest in 2007 and has scored 83 goals in 194 league appearances for the Blues.
His goals helped fire the Spireites to the League Two title during the 2010/11 campaign and last season the 37-year-old was part of the squad that won the Johnstone's Paint Trophy at Wembley.
Chief executive Chris Turner had said in January that he was confident of sorting a new deal for Lester, who has struggled to secure a starting role in Cook's team this season but still leads the scoring charts with nine goals in all competitions.