The Sun says Eriksson is monitoring Lehmann's strained situation at the Emirates Stadium - where he has lost his first-team place to Manuel Almunia.
Eriksson wants to add some experience to his goalkeeper choices while Kasper Schmiechel, 20, and Joe Hart, 20, continue their development.
Lehmann, 37, is out of contract with the Gunners at the end of the season and has become frustrated after being forced to play second fiddle to Almunia.
He is also worried about his international place with Germany ahead of next year's Euro 2008 finals in Austria and Switzerland.
Eriksson is prepared to pay around £1million if he can persuade Arsenal to let the player leave in the January transfer window.