Under Levein's stewardship, United currently sit 4th in the SPL and are guaranteed to finish in the top six for the first time in four seasons.
"The manager will have a slightly bigger budget next season than he has had this year," Thompson told the Daily Express.
"We have discussed budgets with the manager for next season, and as you would expect he's already looking to get people on board and putting plans in place for the future."
With the tangerines unlucky to lose out on penalties to Rangers in the CIS Cup Final, Thompson praised the impact his manager has had since joining in 2006.
"He has built a good team on the park so it's a matter of tinkering with it over the summer and hopefully doing that will make the team even better."