Engineering conglomerate Melrose said it is thinking over whether or not to up its bid for Charter International after the target dismissed its first two offers. "Melrose is willing to consider increasing its proposal to reflect any information which demonstrates that it has materially undervalued Charter and justifies such an increase," the firm said.The statement made on Monday came in response to "speculation in certain quarters" that Melrose is looking to bid for Charter without any access to diligence. The firm said that it will not proceed without the access."Melrose has indicated to the Charter Board that with its cooperation it sees this as a speedy, focused confirmatory process."Melrose made a 780p-a-share approach on 29 June and an 840p-a-share bid on 15 July, both of which were rejected by Charter's board on the grounds that they undervalue the firm and its prospects.Melrose, which recently appointed a new chief executive officer, said that it "reserves the right to waive any other pre-condition to the making of an offer. There can be no certainty any offer will be made even if the pre-conditions are satisfied or waived."It was announced on 15 July that Gareth Rhys was chosen to head the firm with immediate effect, filling the position left open by its previous head Michael Foster, who resigned after the company's disappointing performance. Melrose's shares edged 0.27% higher to trade at 369p by 12:16, while Charter rose 1.15% to 795p.BC