Bright told talkSPORT: "Nobody is in the dark about this, everyone is just waiting for the announcement.
"I'm sure all the contracts are being sorted out now, if it isn't revealed tonight then I think it'll be [Wednesday] morning. There certainly won't be a four-week wait like when Holloway left.
"The players just want someone appointed as quickly as possible, they don't want to hang around for as long as they did before Tony came in, and I'm sure an announcement will be made within the next 24 hours."
Pulis replaced Ian Holloway last season with the club in the relegation zone before guiding them to a 12th-place finish in the league.