The England midfielder was released by Chelsea on a free transfer on the eve of the World Cup.
Enlarge Up for grabs: Joe Cole is available on a free after leaving Chelsea
Cole insists that his focus is solely on the finals as he attempts to secure a place in Fabio Capello's starting XI to face the United States in Rustenburg on Saturday.
But it is understood that Arsenal are leading the chase for Cole, who is regarded as a bargain with his contract over at Chelsea.
Gunners boss Arsene Wenger, who is braced to lose his captain Cesc Fabregas to Barcelona this summer, is keen to sign the former West Ham youngster to boost his attacking options.
Focus: Cole in England action
'I like him as a player because when he played against us he always did a lot of damage against Arsenal,' Wenger told Sky Sports News.
'He can create impact through his creative play. He can dribble, he can pass, he can score goals.'
Cole, who was pushed out of Chelsea after failing to agree an increase on his £80,000-a-week wages, is understood to have been offered a three-year deal at the Emirates worth around £90,000-a-week.
Claims that Cole has finalised the deal with Arsenal are premature but they have jumped ahead of Manchester United and Tottenham in the queue.
United boss Sir Alex Ferguson is a huge admirer of the star, while Spurs manager Harry Redknapp has admitted his is desperate to be reunited with him at White Hart Lane. Redknapp played a major role in Cole's emergence at West Ham in the 90s.
Both United and Tottenham are monitoring the situation and may have to act quickly to stop Arsenal wrapping up a quick deal.
Although Cole is busy with England in SOuth Africa, his agent David Geiss is handling affairs over his future.
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