The former Tottenham boss faces competition from other candidates but has emerged as a leading contender to replace Pepe Mel.
The Baggies' hunt for Mel's successor looks set to extend into a fifth week with interviews expected to continue beyond the weekend.
But Sherwood, who left Spurs at the end of the season following a brief but colourful spell at the helm, is the first name confirmed on the Hawthorns shortlist and is now among the favourites to land the role.
The 45-year-old is expected to hold further talks with the Hawthorns hierarchy in the coming days with the Baggies hoping to make an appointment sometime next week.
Other names remain in the frame with former caretaker boss Keith Downing still under consideration, although he is not thought to have been interviewed formally yet.
Sherwood's outspoken comments during his time in charge at Spurs appeared to make him an unlikely contender to replace Mel, who left almost four weeks ago following an ill-fated tenure that saw the Baggies avoid relegation by just three points.
But news that Sherwood has now held formal discussions with Albion officials suggests chairman Jeremy Peace is willing to consider breaking the mould of recent appointments. Sherwood is keen to test his coaching mettle away from Spurs, where he worked successfully as a coach and consultant but felt he was unfairly judged during his spell as first-team chief.
Spurs ended the campaign 10 points adrift of fourth-placed north London rivals Arsenal – a gap deemed unacceptable by White Hart Lane chairman Daniel Levy.
But in his five months in charge, Sherwood had a top-flight win percentage of 59 per cent – the best of any Tottenham boss in Premier League history.
And a sixth-place finish was enough to get the club into next season's Europa League.
Albion are keen to press ahead with an appointment to ease concerns behind the scenes that delays could scupper their summer transfer plans.
Speculation across Europe last night continued linking them with potential targets, although rumours of interest in Peru international Cristian Benavente, of Real Madrid, Armenia forward Yura Movsisyan, of Spartak Moscow, and former Villa midfielder Steve Sidwell are wide of the mark.
Meanwhile, defender Liam Ridgewell, who was released by Albion at the end of the season, is a potential target for MLS side Portland Timbers.