If he lands the Celtic manager's job, it will be the biggest catch of his life.
Certainly, the Parkhead club are keen to bite, having seen Henrik Larsson and Roy Keane slip off the hook since Neil Lennon decided to call time on his years swimming in the goldfish bowl which is Glasgow.
However, sources at the club are eager to emphasise this is no done deal.
Given the bloodied nose they received in their pursuit of Keane, that note of caution is understandable.
Having finally exited the period of gardening leave imposed by West Brom when they removed him from the manager's seat at the Hawthorns, the 50- year-old is very much a man in demand.
Brighton - with ambitions to build on this season's play-off place and reach the Premier League - are hot on his trail.
Celtic hope that offering the chance to manage a club he has always held dear at Champions League level can counter the pull of cash-rich clubs down south, where Clarke has been working since he left St Mirren to join Chelsea in 1987.
He made his name as a quiet-but-important player during 11 years at Stamford Bridge, where he is proud to hold eighth place in their list of all-time appearances.
The same qualities transferred to coaching when he eventually hung up his boots.
Clarke has been a right-hand man in demand, working as assistant to such luminaries as Ruud Gullit, Jose Mourinho, Avram Grant, Gianfranco Zola and Kenny Dalglish at Newcastle, Chelsea, West Ham and Liverpool.
Finally, in 2012, with his CV showing just one game in charge - while he was caretaker boss at St James' after Gullit departed the 'Toon - it was time for Clarke to become his own boss, and he took over at West Brom.
He is savvy enough to recognise that, having worked under some of the very best, he has much work to do to truly emerge from the shadows.
"Managers like Jose have such a profile in the media, the questions will always be about my time working with him," he reflected.
"Hopefully, in a few years, they're talking about Steve Clarke, the manager or the head coach."
Like a blueprint for success, the time-served instrument technician lays out his philosophy on the game to achieve this recognition.
"I want to be in charge of a good team, one that plays football to excite the public," he said.
"If it was only fantasy football, everyone would play like Barcelona. But it's a results-driven industry."
Clarke has been itching to return to a top position since he was removed from office at the Hawthorns in December.
It had begun well, with a record eighth-place finish in the Premier League. But the second season showed this for the over-achievement it was, and, after some disappointing results, he was sacked and replaced by Pepe Mel.
It was not the first time Clarke felt he had been treated harshly. Having served Chelsea so well as a player then assistant to Mourinho and his successor, Grant, he was upset to be sidelined when Luiz Felipe Scolari and his entourage breezed into town.
Likewise, when Dalglish was removed at Liverpool, the former Celt urged Clarke not to do anything hasty because he felt the new boss, Brendan Rodgers, might have a place for him.
But, before the Rodgers regime got into situ, Clarke was dismissed.
All of which has served not to leave him bitter, but more experienced, and better placed to grasp an opportunity such as Celtic look ready to offer.