Bess's contract at Somerset expires at the end of the 2020 season, and ESPNcricinfo understands that Warwickshire see him as a potential long-term replacement for the retiring Jeetan Patel. The club's sport director Paul Farbrace is known to be an admirer from his time working with Bess as England's assistant coach, and is hopeful that the prospect of first-team cricket in all formats might lure him to Edgbaston.
From this season, counties are no longer required to give 28 days' notice to other clubs before entering negotiations with an out-of-contract player, and have been free to do so since the beginning of June. It is understood that Warwickshire are yet to make a formal approach to Somerset or to Bess's agent, but that they are likely to do so later in the summer.
Bess spent two months of last season on loan at Yorkshire, playing four County Championship games and six T20s. Head coach Andrew Gale said at the time that the club would "try everything we can" to sign him permanently, but the situation is complicated this year by the fact 12 players at the club are out of contract at a time when funds are limited due to the implications of the Covid-19 pandemic.
There may be several contributing factors when Bess makes his decision whether or not to stay at Taunton. He is currently Somerset's second-choice red-ball spinner behind Jack Leach, whose contract runs until 2022, but they are competing against one another - and Moeen Ali - for a place in England's Test team.
Neither player is currently on a central contract - Leach was awarded an incremental contract for 2019-20, meaning the ECB top up his county salary - but both will hope to win one for 2020-21 if they can hold down a spot this summer.
Bess also has ambitions to play white-ball cricket, but has only made four limited-overs appearances (three 50-over, one T20) for Somerset to date. Max Waller, Somerset's main T20 spinner, is also out of contract at the end of the year, while allrounder Roelof van der Merwe's deal runs until 2021. It also remains to be seen whether Bess would want move to the Midlands, having bought a house in Taunton two years ago.
Another promising bowler whose contract expires at the end of the season is Mason Crane, the Hampshire legspinner. Crane has had a frustrating two years with injuries, but was part of the initial 55-man training group named by England in May and will come into contention for the ODI series against Ireland at the end of the month. He was expecting to focus on white-ball cricket this year after Hampshire signed Nathan Lyon to complement Liam Dawson in their Championship side, but the opportunity to play across formats elsewhere could turn his head.
Somerset may also face a battle to keep hold of the Overton twins, Craig and Jamie. Both players' contracts expire at the end of the season, and are sure to attract interest from any clubs in a financial position to offer them a deal. Somerset declined to comment.