The 20-year-old fought on the undercard to Warren's event at the Telford International Centre on Saturday and stopped his opponent Luke Merrifield in the third round to take his record to 4-0.
Thompson, who's brother Liam Davies is signed with Queensberry, hoped his performance would be an audition for a deal and he has now revealed to the Shopshire Star that he is in talks over a contract.
"They've approached my manager so I might have a contract to negotiate for soon. We'll see what happens," he said.
"He's one of the best promoters in the business so it's nice to have that platform. There's a lot of good fighters to follow – the likes of Tyson Fury and of course Liam, who I am always looking up to.
"The stoppage looks good for me, it's what people want to see and hopefully it was eye-catching and that's why they'll hopefully send out a good contract."
Fighting in his home town for the first time in his professional career, Thompson was originally due to face Francisco Rodriguez.
The Spaniard pulled out just days before the event and Thompson was forced to move up to super-bantamweight to stay on the show.
"Rodriguez pulled out a few days before the fight and I needed someone to step in – and I needed to go up a bit of weight too," he added.
"The few days leading up to the fight were a bit crazy to be honest. I was a bit unsure if we would be able to get a replacement and that's why I took the fight at the higher weight.
"We asked everyone at my weight and no-one would step in, that's why I jumped up the weight and luckily someone stepped in and I was still able to fight.
"I was going to do anything I could to be on the show and it still worked out perfectly for me.
"I'm very happy, it couldn't have gone much better. It was a punch-perfect night. I felt good throughout the fight and felt strong.
"It was one of the best night's I've had as a boxer so far. The support was brilliant and I felt at home.
"I had to take a risk and look at the reward, and I was confident enough to take it with both hands."