you don't suppose i could talk to you into it,do you?

you don't suppose i could talk to you into it,do you?
02年8月份老托福听力里面的句子,
原话：I'm going to be out of town all next week,and I’m looking for someone to feed my cat while I'm gone,you don't suppose i could talk to you into it,do you
You know,I’d be glad to,but I’ll be away next week too,but you know what,let me give my sister a call,she loves animals,and she lives only a couple of blocks from your apartment.