The Association said Natural England should be looking at ways to improve access already in place, and concentrate on providing good quality, permissive and educational access.
The costs associated with access provision and ongoing maintenance will require continuous funding if these proposals form part of the New Environmental Land Management Scheme.
CLA President Harry Cotterell said: "Natural England seem to have the desire to fund access by offering short-term compensation in return for a permanent consent, which is clearly wrong.
"There is a very real fear that such schemes would increase the demand for funds, reducing money spent on other areas or leading to further modulation of payments made to farmers under CAP reform.
"We support well-managed voluntary permissive access and access for education particularly, but there has to be an element of realism, especially at a time when local authorities do not have the funds to maintain what is there already.
"At a time of departmental cuts, additional permanent access is not something that we should be considering and is a real diversion from the core aims of CAP reform."