4:37PM BST 21 Jul 2011
Arsenal made a £10million offer to take the 28-year-old to the Emirates Stadium which was rejected out of hand.
It is understood that was £2million lower than the one made 12 months ago.
Everton view the bid as being well below the player's market value, particularly as the defender signed a new four-year contract in March.
The Merseyside club have yet to make any signings so far this summer and their tight finances means manager David Moyes is likely to have to sell players in order to be able to bring in new faces.
But Jagielka is not one of those on the list which the Toffees boss is looking to offload, although should a bid closer to the club's valuation of about £20million come in they would have to seriously consider it.