Scudamore, who is stepping down after 19 years with the Premier League, is reportedly paid £2.5 million (A$4.5 million) a season.
According to the BBC, the clubs were asked in a meeting on Tuesday for the 'gift' by Chelsea chairman Bruce Buck.
Under Scudamore, the Premier League's value in terms of television rights has dramatically improved, from £670 million (A$1.2 billion) when he joined to the latest deal worth £5.14 billion (A$9.3 billion).
The report comes against the backdrop of a funding crisis for grassroots in England.
Just last month, it was proposed by England's FA that they sell Wembley Stadium in order to help fund grassroots projects.
Scudamore will be stepping down in December and will be replaced by Susanna Dinnage.
Dinnage joins the world's richest domestic league from media organisation Discovery.