Ljungberg's contract with Calvin Klein runs to next summer, when the England captain would take over if he accepts the approach from CK, which was revealed over the weekend.
Reports said England skipper and Real Madrid star Beckham had agreed to do a photoshoot for Calvin Klein and that the deal was close to being finalised.
News of the deal comes after it was revealed last week that Beckham spends 拢1,000 a month on 60 pairs of CK underwear, which he wears once before throwing away.
Ljungberg has been CK's frontman since first appearing in an ad in autumn 2003, and a two-year extension to the contract worth 拢500,000 was signed last July.
Ljungberg appears in a new series of ads with Russian model Natalia Vodiana for an international campaign being rolled out this month. Critics suggested Ljungberg's previous solo campaign for CK featuring Ljunberg lounging in just pants were too homoerotic.
The new ads were the first time a couple had starred in a CK ad since Kate Moss and Mark Wahlberg modelled together in the early 90s.
Beckham already has multimillion-pound sponsorship deals with Adidas, Gillette, Pepsi and Police sunglasses, and launched his own perfume Instinct last November.
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