Manchester United are expected to return with separate offers for Marouane Fellaini and Leighton Baines, having incensed Everton with a joint £28m bid for David Moyes's former players.

Everton described as "derisory and insulting" an offer that valued Fellaini at £16m, a decrease on what Moyes paid for the midfielder five years ago, and Baines at £12m, the sum rejected earlier in the summer. The offer was made late last week by United's executive vice-president Ed Woodward but sanctioned by Moyes, leaving Everton's chairman, Bill Kenwright, furious at the valuation and its potential disruption to Roberto Martínez's debut season at Goodison Park.

United's joint bid, as with their initial move for Baines in June, was rejected out of hand by Everton but is unlikely to be their last approach having failed to make any senior signings so far under Moyes. Everton are adamant the England left-back is not for sale and want to keep Fellaini, although an improved offer for the Belgium midfielder may test that resolve. United's prospects would therefore be improved by lodging separate bids for Everton's prize assets.

Everton's director of communications, Alan Myers, said: "Everton received bids from Manchester United for two players. Those bids were immediately rejected out of hand as derisory and insulting. The club did not make public these details as it was vital Roberto Martínez's preparations for the opening game of the Premier League season were not disrupted in any way."

Martínez may return to Wigan Athletic for James McCarthy in the event of Fellaini's departure and has inquired about signing Gareth Barry on a season-long loan from Manchester City. However, the Everton manager says the club have complete control over Fellaini's future following the expiry of a £23.5m buy-out clause in the midfielder's contract on 31 July and will not sell below that price. The 25-year-old did not attract one offer while his buyout clause was in place, strengthening United's conviction that £23.5m did not reflect his market value.

Everton had anticipated a lower offer from United after 31 July and it was only last Thursday, before the joint bid was made, that Martínez stated: "When you are in a strong position financially you will never sell a player for less than the buy-out clause." Nevertheless the £16m valuation of Fellaini stunned Everton. The Belgium midfielder was signed by Moyes from Standard Liège for £15m in 2008, a fee that rose to £17.5m with add-ons. Liège are entitled to 20% of any profit that Everton make on Fellaini and the Goodison club had wanted a £30m release clause written into his last contract.

United have struggled in Moyes's and Woodward's first transfer window together at Old Trafford with the club's pursuit of Cesc Fabregas, the manager's prime target, unlikely to succeed after the midfielder spoke publicly about his desire to stay at Barcelona.

Martinez did not rule out the prospect of selling Fellaini when he outlined the midfielder's contractual position at Everton last week, saying "If there is an offer on the table then we will have to look into it,", but will be distinctly unimpressed by Moyes' refusal to accept defeat on Baines. United told Everton their £12m move for Baines in July was a final offer and the decision to re-submit the bid has added to the annoyance at Goodison Park.