Price was knocked out in the second round by Thompson last month, losing his unbeaten record in the process.
The pair will clash again at the Echo Arena in Liverpool on July 6, with Price revealing that Lewis told him to avenge the defeat quickly.
He told the Daily Star: "I could have taken on opponents of a lower standard but I wanted to get right back, and Lennox agreed with me.
"I asked him what he would have done if he had been given the chance to fight Oliver McCall straight after he had lost to him. He said without any hesitation, 'of course I would', because he would have loved the chance and that advice is good enough for me.
"Lennox told me that fighting Thompson again so soon after our fight would take a lot of weight off my shoulders."
The 29-year-old has a single blemish on his 16-fight professional record.