The Boynesiders enjoy a favourable record over the Candystripes in recent years but Cooke is not taking anything for granted this Friday evening
The Drogs are unbeaten against the Foylesiders in their last seven meetings and this season they have won once and drawn twice. However, Cooke believes that the Airtricity Premier Division clash between the sides at Hunky Dorys Park will be "tough".
"Friday night is going to be tough," he told the club's official website. "We've played each other three times already this season so there is a level of familiarity between the squads.
"Derry will be coming to Drogheda looking to get one over on us. Declan has done a good job at the Brandywell and it's no surprise that they are in the top three.
"We've had a few good results over Derry in our last meetings, but we won't take any game for granted."
Stephen Quigley is Drogheda's only injury concern, but Derry City have a defensive headache to contend with as Dermot McCaffrey serves a suspension and Thomas Crawley struggles to recover from injury.
The Candystripes have lost significant ground in the title race after suffering two consecutive league defeats, but manager Declan Devine is not concerned with "recent records".
"As far as recent records are concerned they go out the window as soon as we take to the pitch and we will as always prepare to try and win what we have no doubt will be a very physical battle on Friday evening," he told the club's official website.
Drogheda United host Derry City in the Airtricity Premier Division on Friday, May 17. Kick off 19:45 BST.