Ben Haim, 23, has emerged as a top Premiership player since joining in a £150,000 move from Maccabi Tel Aviv in the summer of 2004.
But Bolton boss Sam Allardyce has spoken out to quell rumours about a possible move for Ben Haim.
Speaking to Wanderers' official website, he insisted, "He is a vital member of our first team and is not available for transfer."
Meanwhile, Arsenal could try and land Bolton keeper Jussi Jaaskelainen on a free transfer.
The Mirror says Jaaskelainen verbally agreed revised terms at the Reebok, but has yet to sign and could buy out the remaining 18 months on his contract and recoup the money as a signing-on fee.
Gunners boss Arsene Wenger is a long-time admirer of the 30-year-old Finn, who was linked with Manchester United before Edwin van der Sar's arrival.