The Yorkshire all-rounder has been performing well in the shop window known as the T20 Blast.
Each of the eight teams in The Hundred can add a “wild card” selection to their squad next month.
It means that men such as Thompson, who were not picked up in the initial draft, could yet feature in the competition.
“I can’t say that it’s not on my mind,” said Thompson, who furthered his claims with a blistering innings of 66 not out from 28 balls in Wednesday’s win against Worcestershire.
“I’ve obviously thought about it and seen that the wild card spots are available.
“Whether I’m playing well enough at the moment, you never know… Obviously, it would be lovely to get picked up in it, both for the experience and for the quality of players that are going to be playing in it.
“I’m hopeful, but we’ll just have to see what happens.”
Thompson, 24, said that he had never played better, or hit the ball more cleanly, than he did in the game against Worcestershire.
The left-hander shared an English record T20 sixth-wicket stand of 141 unbroken with Harry Brook, who hit 83, and who is one of six Yorkshire players in the Northern Superchargers squad that is based at Emerald Headingley for the 100-ball event.
Whether Thompson would be an attractive proposition for Superchargers remains to be seen; they might look for cover in other areas and they also need to replace Olly Stone, the England fast bowler who was recently diagnosed with a stress fracture of the back.
Aaron Finch, the former Yorkshire batsman and the Superchargers captain, is also expected to withdraw from the competition due to his Australian white-ball commitments.
The other Yorkshire players in the Superchargers’ squad are Adil Rashid, David Willey, Adam Lyth, Tom Kohler-Cadmore and Matthew Fisher.
In addition, Joe Root and Dawid Malan are playing for Trent Rockets, Jonny Bairstow for Welsh Fire and Lockie Ferguson for Manchester Originals.
The men’s Hundred runs from July 22 to August 21, with the women’s event starting a day earlier. The Hundred clashes with the 50-over Cup, now a glorified second XI competition that runs from July 22 to August 19.
“Wild card” players are set to be named on July 2 and receive the lowest salary band of £24,000.