Cheltenham chairman Paul Baker says manager Mark Yates will be able to use their FA Cup money to buy new players.
The Robins booked a third-round meeting with Everton after beating
Hereford 2-1 in Tuesday's replay.
The League Two club will net £135,000 from their televised game with the Premier League side, to add to the £113,000 they have already accumulated in TV rights and prize money.
And Baker said he will "support" Yates in the January transfer window.
"Mark's got much more of a chance of us saying yes after winning this game," he told BBC Gloucestershire.
"It's going to be really difficult for me and the board to turn down a request from Mark to strengthen the squad in January.
Cheltenham's FA Cup fortunes
- for winning first round
- for winning second round
- for second round television rights
- for third round television rights
"We want to do that but we'll do it sensibly. This is an opportunity to clear some debt and to stabilise the football club."
Cheltenham went on a similar run in the Cup last season - seeing off
Tottenham at White Hart Lane
in the third round.
They lost the game 3-0 but the prize money allowed them
to buy influential winger Jermaine McGlashan
from Aldershot, for a fee thought to be around £70,000.
The Robins went on to reach the League Two play-off finals at Wembley in May -
where they lost 2-0 to Crewe
- and Baker says repeating that feat is still their priority.
"Like Tottenham last year, we'll go down and enjoy it," he added.
"Our focus has got to be on promotion and this game will only help that."