The Premier League players met the musician backstage on the night that he performed at Liverpool's Echo Arena.
Nasri and Sturridge posted photos of themselves on Instagram separately handing Drake a signed City and Liverpool shirt respectively.
Nasri accompanied the image with the message: "Thanks @champagnepapi for looking after us last night #greatshow #drizzy #ReppinMCFC"
Sturridge wrote on his account: "Was a good vibe chopping it up with @champagnepapi about music and football. He did his ting.. #OVO #redordead."