Mr Heseltine, MP for Henley in Oxfordshire, and colleagues including local government minister David Curry will hear the pleas of councillors demanding more government money for Oxfordshire or permission for the county council to raise the cash itself.
The delegation is trying to head off a projected £12m of cuts in the coming financial year. If the government refuses to make up the shortfall, the county council wants to raise more money by increasing council tax by more than the current 7% limit.
Meanwhile, a Sheffield City Council delegation today also meets Mr Curry and will tell him to maintain services at their present level would need £35m more than the government has allowed.
Although the Sheffield spending limit has been increased by 2.1%, this is well below the current inflation rate and less than for most other metropolitan districts and all shire counties, the council said in a statement.