Jago only returned to his post at Tesco this week, but has already been linked to the chain, which is hunting for a new chief executive following the departure of Steve Lewis.
Headhunters have been meeting potential candidates and Jago is understood to have been invited to discuss the position.
Jago returned to Tesco on Monday (March 9) following a four-month suspension after he was asked to step aside as BWS head amid an investigation into a £250 million black hole.
He was reinstated and given a new position of category director – group wine, and has played down rumours he could be poised to leave.
Speaking to OLN, he said: “I’m delighted to be back and I am always committed to what [the job] I’m doing.
“I couldn’t comment [about Majestic rumours], but it is always flattering to be thought of in relation to any complex problem and as someone that could play a part in solving it.
“I know Steve Lewis very well and I think he did a fantastic job. But it is quite possible that a new set of ideas is what’s needed, as with many other wine businesses, to reinvent itself.
“But it’s not my job. It’s the decision of the chairman and board of directors.”
Jago said his new Tesco role was more focused on strategy than “wheeling out a new own-label wine range”.
He dismissed rumours that he had returned to Tesco in a reduced capacity after Gavin Warburton, who oversaw the department in Jago’s absence, was promoted to UK category director for beers, wine and spirits.
He said: “My role gives me a unique opportunity to look at where Tesco’s wine business is going to be in two or three years’ time. It’s a chance to step back from the frontline trading environment and set out a vision.”
Majestic refused to comment on candidates involved in the recruitment process.
However, a leading wine supplier said: “Dan would be a great fit for Majestic, much better than for the job he’s doing at Tesco. Supermarkets are no longer focusing on fine and premium wines and with his background as head of Bibendum, he would surely be a strong candidate. Tesco is a different place now, but in returning, he has cleared his name and can consider his options about where his career goes next.”