I would say 'at the same price' or possibly 'for the same price'. However 'rate' might be a better word than price in this context.

It's an awkward sounding sentence even with the word 'with'. "On" and 'in" would not work. Can you change the sentence? I'd say: "He is renting the shop to me and is asking the same price as last year."

Why doesn’t need for articles? I believe he meant in the last year as in 2016 for instance

Not part of your question, but no article is needed before next year. "He rents the shop to me at/for the same price as last year"

Wendy is right, but I think "at the same price" would work here as well.