Gloucestershire police said thieves entered rooms at the team's Swindon Village base on Sunday and stole wallets, mobile phones, watches and car keys.
They said two 17-year-old local youths had been arrested on suspicion of theft and released on bail. Some of the stolen items were recovered.
Cheltenham striker Daryl Duffy vented his anger on Twitter while also saying he would be willing to buy back his stolen phone to recover photos and video of his children.
Monday's match will be one of the biggest in Cheltenham's history with the League Two club, ranked 66 places below five-times winners Everton, seeking to reach the fourth round for only the third time.