Bristol say they will "take all reasonable actions" after denying a deal had been done with the Rugby Football Union for Steve Borthwick to become England forwards coach.
The RFU released a statement saying former England captain Borthwick would join new head coach Eddie Jones' team.
Borthwick signed a long-term deal with Bristol after the World Cup, having worked under Jones with Japan.
"We have not agreed Steve Borthwick can leave our employment," Bristol said.
Borthwick is understood to have handed in his resignation on Tuesday, but the club said 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.
In the same RFU statement, Jones described Borthwick as a "great addition" who would "get the best out of the players at the highest level".
Jones also called Borthwick a "young coach with great potential" and praised his "analytical" approach as part of the RFU announcement.
Borthwick, 36, captained both Bath and Saracens during a 16-year playing career and won 57 England caps between 2001 and 2010.
The lock was part of the England side that reached the 2007 Rugby World Cup final in France and was appointed captain by then coach Martin Johnson in 2008.
Borthwick worked part-time with Jones for two years as a spot coach with Japan, before retiring in 2014 - with a record 265 Premiership appearances - and becoming the country's full-time forwards coach.
He helped Jones to mastermind Japan's stunning victory over South Africa in this year's Rugby World Cup before signing a contract with Bristol.
Jones, who also worked with Borthwick at Premiership side Saracens, was named as Stuart Lancaster's successor in November, following England's dismal World Cup campaign.
Jones, 55, will take charge of his first match on 9 February when England face Scotland in the Six Nations.
Others in contention
Jones is also looking to name replacements for previous attack coach Catt and defence coach Farrell.
The former Australia head coach has asked another former colleague Paul Gustard to join his team, with the Saracens defence and forwards coach currently considering the offer.
Northampton director of rugby Jim Mallinder told BBC Sport that backs coach Alex King will meet Jones this week to discuss a position with England.
Mallinder says there has been no official approach yet from the RFU, but that Saints will not prevent King from leaving if he was offered a role.