The Spaniard is currently preparing to get Newcastle United back into the Premier League.
Liverpool manager Juergen Klopp and Newcastle manager Rafael Benitez
Former Liverpool duo Phil Babb and Neil Mellor have been discussing potential England candidates on LFC TV, and ex defender Babb mentioned one individual who has not been discussed in the press, even if his club Newcastle United wouldn't like it very much.
The 45-year-old suggested Reds favourite Rafa Benitez, who famously won the Champions League with Liverpool in 2005, would be a superb candidate for the vacancy following on from England's shock loss to Iceland.
"Rafa’s got vast experience hasn’t he and he’s dealt with English players before," Babb told LFC TV. "He’s never really failed wherever he’s been, what a great candidate.
Newcastle manager Rafael Benitez before the match
"Would he take it, would he leave Newcastle? Possibly."
The ex-Republic of Ireland defender played for the Reds for six years, before heading to Portugal for a couple of seasons and retiring from playing after a short spell at Sunderland, but he may be even more unpopular on Tyneside after his suggestion.
LFC TV (@LFCTV) June 30, 2016
The Spaniard delighted Newcastle fans with his commitment to the Magpies despite their relegation last season. Benitez did well in difficult circumstances after taking over at St James's Park, finishing the campaign with the astonishing 5-1 win over title challengers Spurs on the last day of the season, despite already being down.
With Benitez being given more control at the club than previous managers, Newcastle have as good a chance as they have had in years of making serious progress - even if they are starting with the handicap that sees them in the Championship next season.
England's Wayne Rooney reacts
However, equally, the English national team is in its own problem after yet another disastrous tournament.
The former Liverpool and Real Madrid manager may be unwilling to jump ship so soon after committing to the Magpies, which would be admirable in today's game, but if England really pushed hard for him, who knows for certain what the outcome will be.