Everton want Ronald Koeman to succeed Roberto Martínez and hope to lure the Southampton coach with the promise of the biggest transfer budget in their history.

Farhad Moshiri, Everton’s new major shareholder, sacked Martínez on Thursday and has earmarked Southampton’s manager as his preferred replacement. The British-Iranian billionaire faces a challenge to prise the 53-year-old from St Mary’s, however, even with Koeman yet to commit to a new contract and having just over 12 months remaining on his deal.

But Everton hope a transfer budget swelled by Moshiri’s investment, the new broadcasting deal and lucrative player sales – with Romelu Lukaku and John Stones likely to leave this summer – will persuade Koeman to move to Goodison Park.

Koeman’s agent is Guido Albers who, intriguingly, touted another of his clients – Frank de Boer – for the Everton job last weekend. Ajax announced on Thursday that De Boer is to leave in the aftermath of their failure to make it five titles in a row on the final day of the Eredivisie season, losing out to PSV Eindhoven .

De Boer, who won four league titles during his five and a half years with the Amsterdam club, is also under consideration by the Everton board. Albers said the 45-year-old “would love to join a club like Everton” but there has been no approach for the former Holland defender so far. De Boer will join Ajax on their end‑of‑season tour of China on Friday and part company on their return next Thursday.

Moshiri brought Martínez’s three-year reign to an end following a dire run of form, a second poor Premier League season and clear evidence of support for the manager draining from the fanbase, players and the boardroom, although the chairman, Bill Kenwright, was reluctant to part company with the former Wigan Athletic manager.

Everton have won only one of their past 10 matches and their latest anaemic away performance, Wednesday’s 3-0 reverse at Sunderland, came with the manager demanding a reaction to a feeble 3-1 loss at LeicesterCity on Saturday.

Martínez and his players were on a scheduled day off from the club’s Finch Farm training ground on Thursday, when the board discussed his position once again. It had been precarious since April, when what the Catalan had described as a “defining week” produced a shambolic defeat at Liverpool in the derby plus a stoppage-time loss to Manchester United in the FA Cup semi-final.

The decision was taken on Thursday to spare the 42-year-old from a hostile Goodison in the final game of the Premier League season on Sunday. Everton also postponed the club’send-of-season awards dinner at St George’s Hall on Thursday in the wake of the sacking after some fans planned to protest against the running of the club. Duncan Ferguson and David Unsworth, the first-team coach and under-21 coach respectively, will take charge of the final game against relegated Norwich City, along with the former manager and striker Joe Royle.

“Everton Football Club regrets to announce that Roberto Martínez has left his position as first-team manager with immediate effect,” said a statement. “The chairman and the board of directors would like to place on record their thanks for the dedication and commitment Roberto has shown during his three seasons with the club. Roberto has been a great ambassador, conducting himself, at all times, with the utmost integrity and dignity. He secured the club its highest ever Premier League points total, a place in the last 16 of the Europa League and appearances in both domestic cup semi-finals. He has also played a key role in the development of several young players, managing their progression to the Everton first team and international honours.”

Confirmation of Martínez’s departure followed the resolution of talks between Everton and the Spaniard’s representatives over a severance payment. The manager had three years remaining on the lucrative contract he was given by Everton at the end of his first season in 2014. He is believed to have earned at least £3m a year and the club will be left with a substantial severance payment for him and his backroom staff. The assistant manager, Graeme Jones, is believed to have already left while the first-team development coach, Dennis Lawrence, goalkeeping coach, Inaki Bergara, and chief scout, Kevin Reeves, are also expected to leave.

Everton are 12th in the Premier League and lost both of this season’s domestic cup semi-finals. Last season’s 11th-place finish was their lowest in nine years and having won 21 league games during his debut campaign, Martínez oversaw only 22 league wins in the past two seasons. The former manager has worked tirelessly on improving the academy and training-ground facilities but results cost him support and ultimately his job.