Chelsea have made it clear that Sturridge, who scored his fourth goal in four games on Saturday to earn Bolton a 1-1 draw at Newcastle, is not for sale but Coyle is hoping to renew the loan deal.
"I would love him to stay here. I have said, 'Come in, enjoy your football, play with a smile on your face and see where that takes you'," Coyle told The Sun. "I would love his loan to continue next season.
"I was close to getting Jack Wilshere back at the start of the season but Arsenal had a few injuries. He got his chance there and set the place alight. Who is to say Daniel cannot do the same?"
Chelsea signed Sturridge, 21, from Manchester City in July 2009 after his contract expired. A tribunal set a fee of £3.5 million as compensation for his development at Eastlands.