Bristol say they have not reached a deal with the Rugby Football Union over the appointment of Steve Borthwick as England forwards coach.
The RFU earlier released a statement confirming former England captain Borthwick will join new head coach Eddie Jones' backroom team.
Borthwick joined Bristol as forwards coach after the World Cup, having worked under Jones with Japan.
"We have not agreed Steve Borthwick can leave our employment," said Bristol.
Borthwick is understood to have handed in his resignation on Tuesday, but the club added they had not given the RFU permission to speak to Borthwick and would "take all reasonable actions as necessary to protect the club's position".
Before Bristol intervened, Borthwick was quoted in an RFU statement saying it was a "huge honour to be asked as these chances don't come around often".
The former England captain was due to be Jones' first appointment after previous forwards coach Graham Rowntree departed on Monday, along with Mike Catt and Andy Farrell.
"Steve has a huge amount of international experience as a player and a captain and his coaching in Japan in recent years shows he can get the best out of the players at the highest level," said Jones, prior to Bristol's response.
"He is a great addition and I look forward to working with him again as we look ahead to the start of the Six Nations next year."
Jones also called Borthwick a "young coach with great potential" and praised his "analytical" approach as part of the RFU announcement.