Manchester United on Thursday night had an increased bid of £36m rejected for Marouane Fellaini and Leighton Baines as David Moyes continues to pursue his former players at Everton.

United failed with a £28m joint offer for the Belgium midfielder and England left-back a fortnight ago, with Everton labelling a deal that valued Fellaini at £16m and Baines at £12m "derisory and insulting". The Premier League champions have returned with an improved offer but again found Everton unwilling to sell, although talks are likely to continue between Moyes and the Goodison Park chairman, Bill Kenwright, before Monday's transfer deadline. Moyes's successor as Everton manager, Roberto Martínez, said he was unaware of a renewed United bid for his players on Thursday but pointedly admitted that Kenwright will have the final say on transfers at the club.

Fellaini had a £23.5m buyout clause in his contract that expired on 31 July and, though Martínez has said Everton will not sell for less, that clause is reactivated in January. United have now had three offers rejected for Baines and may ultimately have more success with an individual bid for Fellaini. The Everton manager has contingency plans in the event of the midfielder's departure and confirmed an inquiry has been made for James McCarthy at Wigan Athletic.

"I've had conversations but not in a formal way," he said on the £15m-rated McCarthy. Gareth Barry is another midfield target providing a compromise can be reached with Manchester City over his £120,000-a-week wages.

Despite his stance that Everton do not want to sell Baines or Fellaini, Martínez said the club must be "prepared for anything" before Monday's transfer deadline and made the significant admission that negotiations will be left to Kenwright and United. "I am not aware of it," he said of an improved United bid. "I have told the chairman I don't want to know anything that's going on, I only want to know the final news if there is anything.

"I have had enough of 'he said this, he said that'. This is a really sensitive situation because you're talking of a chairman and previous manager [Moyes] who had a relationship over 11 years. A lot of things have been said in public and I don't want to be part of that. I'm out of it. But I have never had any instruction that anything has changed."

Martínez reiterated that the England international Baines had not asked to be allowed to rejoin Moyes at Old Trafford. "No, no," he said. "But whatever the players say in a different situation or environment could change. All I can tell you is that Leighton is an Evertonian and very thankful for the opportunity Everton gave him. And if he has a club like Manchester United interested in him, it's a football compliment and we will take it like that. Then if things are not right, they are not right. Sometimes the club needs to be respected in that way."

Neither Fellaini nor Baines have submitted a transfer request or stated a desire to leave Everton so far but, should they be denied a move to United, Martínez insists he is prepared for the consequence of two potentially frustrated players. "That's the nature of it, and not just an Everton situation," said the manager.

"It's an interesting debate. Do clubs have to keep hold of players in bad moments of form or when they get injuries, and then let them go when they do well? Every time you have a good player do you have to expect to lose them because they think the grass is always greener elsewhere? It can't work like that. You have to be respectful to the club who has given you the opportunity, the club who has made the previous investment. Things need to be right for everyone.

"The competition would die otherwise because Real Madrid and Barcelona would always have the best players, the ones in form. You need to be realistic with football in general. Of course, players will always like that next challenge and to go to play Champions League football and win trophies. But there are great stories about that. Michael Owen leaves Liverpool to go to Real Madrid to win trophies and Liverpool win the Champions League. In football nothing is guaranteed. Clubs need to be strong – and be allowed to be stronger than the players."