The Prime Minister and his wife Sarah want to show their gratitude to the couple for their generosity towards good causes.
When asked if the Beckhams were invited to Chequers, Sarah told reporters: 'Of course'.
'Sarah does a lot of charity work and has previously called on Victoria to help,' an insider reveals.
'They get on well and Sarah knows Victoria and David can be relied upon to send signed books or jeans or give time if possible.'
David, 32, met up with Gordon last month to discuss England's bid for the 2018 World Cup.
In return the Prime Minister visited Becks' football academy in South London.
The two pals and their wives are expected to get together for a 3-night stay at the Chiltern Hills retreat in the near future.
'They are now very good friends,' the source tells The People. 'An invite to Chequers was a natural step.'
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