Frank de Boer is interested in becoming Everton boss and is the "right man for the job", says the Dutchman's brother.
But Ronald de Boer added: "It's not up to him to make the move, that's up to the club."
The Toffees have also been linked with Southampton boss Ronald Koeman and Newcastle manager Rafael Benitez following Roberto Martinez's sacking.
Benitez is an "almost perfect fit" for Everton, former England defender Danny Mills told BBC Radio 5 live.
He said the former Liverpool boss would be open to a return to Merseyside.
"He lives there, his family is there and he'd be happy going back," insisted Mills.
He added it was "not beyond the realms of possibility" that Benitez ended up Everton and Martinez replaced him at Newcastle.
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Martinez, 42, promised to deliver Champions League football for Everton when he replaced David Moyes in the summer of 2013.
He finished fifth in his first campaign in charge with 72 points.
But his side have won just five league games at home in this campaign and will end with their lowest points tally at Goodison Park since 1981.
Ex-boss Joe Royle, who also played for the Toffees for eight years, and former Everton player and current under-21 coach David Unsworth and will take charge for the final game of the season against Norwich City on Sunday.
The case for Benitez
Benitez, 56, started the season with Spanish giants Real Madrid but faces the prospect of the second tier of English football if he remains at Newcastle.
However, it is believed the Spaniard, who took charge of the Magpies in March, has a break clause in his contract.
Newcastle legend Alan Shearer says he would be "amazed" if Benitez remains at St James' Park, but a group of Magpies fans have not given up hope.
They have issued a statement urging him to stay.
"Whilst we fully accept the short-term prospect of life in the Championship may not be as appealing as other offers, we can certainly promise you the potential rewards of the longer term would exceed any position that you consider," it read.
Benitez, who led Liverpool to a Champions League win in 2005, is likely to have a number of offers should he decide to leave.
He also won Fifa's Club World Cup and Italian Super Cup with Inter Milan and guided Chelsea to a Europa League success in 2013.
Ex-Newcastle midfielder Jermaine Jenas says Benitez would not be a good fit for Everton because the fans would not like his defensive brand of football.
The case for De Boer
Frank de Boer led Ajax to four straight league titles between 2011 and 2014 but missed out to PSV Eindhoven on the final day this season.
He is now a free agent after leaving Ajax on Thursday.
As a player, De Boer won the Champions League and Uefa Cup with Ajax, before claiming a La Liga title with Barcelona.
Prior to taking charge of Ajax, the former Rangers defender, 45, was an assistant manager with the Dutch national team.
Michael Ball played alongside defender De Boer at Rangers in 2004 and believes the Dutchman would be "refreshing" for the Toffees.
"He likes to bring a lot of youth into his teams and, with the Everton squad being so young, it could only be a positive for him," said Ball.
"I know he's unproven in England, that's the only negative. I think De Boer would be refreshing for the Premier League and refreshing for Everton."
The case for Koeman
The Dutchman has impressed at Southampton after taking over from Tottenham-bound Mauricio Pochettino in June 2014.
The 53-year-old's side will finish no lower than eighth in the Premier League this season but are hoping to better last season's best-ever finish of seventh and reach the Europa League.
Koeman is well respected, having starred for the Netherlands and Barcelona as a player before embarking on a managerial career that has taken in Ajax, Benfica, PSV Eindhoven, Valencia and Feyenoord.
Southampton centre-half Virgil van Dijk is "confident" Koeman will stay.
"He has done an amazing job so far," said Van Dijk. "Hopefully we can do it next year as well and then it is about him and the club and what he wants to do."
The other contenders
Take your pick from Manuel Pellegrini, Mark Hughes, Brendan Rodgers, Moyes, Martin O'Neill and Unai Emery.
Pellegrini will leave Manchester City at the end of the season, while Hughes has impressed at Stoke City and Rodgers remains out of a job since being sacked by Liverpool in October.
Former Toffees boss Moyes, who spent 11 years in charge at Goodison, is also available after unsuccessful stints at Manchester United and Real Sociedad.
O'Neill will guide the Republic of Ireland at Euro 2016 but has yet to sign a new contract for the 2018 World Cup.
And Emery will secure a hat-trick of Europa League titles with Sevilla if the Spanish side beat Liverpool in this season's final.