• Everton may set Jagielka's price at more than £18m • Valencia also want to keep Mata, valued at £17.5m

Arsène Wenger intends to ease the transfer window frustration of Arsenal supporters with successful moves for the Everton defender Phil Jagielka and the Valencia winger Juan Mata.

The manager has waged a battle throughout the summer to retain his captain, Cesc Fábregas, and the midfielder Samir Nasri, and it has felt, even to a section of the club's board, that he has done so to the detriment of seeking new signings.

Fábregas looks certain to get his long-touted switch to Barcelona – Wenger wants the issue resolved in the coming days – while Nasri is likely to be held to the terms of his contract, which has 12 months to run. He could then depart on a highly lucrative Bosman free transfer.

Wenger has signed the forward Gervinho from Lille for £10.6m, together with the reserve right-back Carl Jenkinson from Charlton Athletic, but many of the club's fans have been desperate to see him make a major impression in the market.

The arrivals of Jagielka and Mata, together with the short-term retention of Nasri, would go some way to answering the critics. Wenger has already seen one bid for Jagielka, of around £12m, rejected by Everton but he is preparing a renewed offer that he hopes will force the Merseysiders' hand.

David Moyes, the Everton manager, has made it clear that Jagielka is one of the few players whom he does not want to sell and it may need an extraordinary offer, of upwards of £18m, to tempt him and his directors.

Wenger wants a commanding central defender with Premier League experience, a player to address Arsenal's achilles heel of set-piece concessions, and Jagielka, the England international, would fit the bill. Wenger has also been linked to Gary Cahill of Bolton Wanderers and Chris Samba of Blackburn Rovers.

Mata would not be a like-for-like replacement for Fábregas. The 23-year-old tends to play on the left, although he could play in a central position. He has emerged as one of Europe's most coveted young players after his starring role for Spain's Under-21s in their triumphant European Championship campaign last month. He was also a part of the victorious senior squad at the World Cup finals last summer.

Wenger has experimented in pre-season with Nasri in an advanced central midfield role, rather than his more accustomed position on the left. Gervinho also likes to come in from the flank.

Valencia do not want to sell Mata, who is valued at £17.5m, but the technical secretary Bralui Vázquez admitted he could not rule out the possibility. "We have a back-up plan in case Juan leaves," he said. "That's not just the case for Juan, though. We have a plan like that for every player. We have to be prepared if something happens."