The South American side, whose name means pirate, won promotion to the top flight this season having won the Copa Peru 2018.
And they want to celebrate by having the Pirates of the Caribbean character permanently on their jerseys.
Various cartoon pirates have appeared on the team's shirt but Molinos favour the face of Captain Jack.
Sparrow is the constantly inebriated star of the billion-dollar film series starring Depp, Keira Knightley and Orlando Bloom.
The club has reached out to the Walt Disney Company for permission through fear of copyright infringement.
And it appears that their request may be agreed.
Molinos president Manuel Aguinaga said: "Disney have asked us to specify the image we want and its dimensions.
"Once we send them the information they'll take a month and a half to evaluate it, and if it's a yes from them we'll start to discuss terms.
"We are not in a position to make a financial contribution to them.
"But if we use Jack Sparrow's image we will be giving Disney free publicity.
"That would be the compensation we give them."
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