There are just too many cases of contractors accepting a permanent role then when a lucrative contract arrives they either fail to take the position they accepted, or jump ship without so much as a by your leave. Understandably MCs are very sceptical of taking contractors into perm roles and take a lot of convincing that they intend to take on a perm role and remain in it for a reasonable tenure.
One thing you can do is show some restraint on salary expectations. Almost without fail the contractor ends up using their day rate as leverage to start demanding escalating salaries on the basis they can earn x amount in a year as a contractor therefore they want y from the perm role.
The smart ones realise it simply doesnt work like that, but if there is an intermediary involved (not just a recruiter/HH but also hiring managers who have pulled strings to get you over the career contractor hurdle) this sudden about face can be embarrassing and damaging.
If you really DO want to return to perm, prepare to take a (possibly significant) financial hit for the security and be sure you really do want to return to a permanent role. Once you are sure on all this, then having a good rationale about why the move into contracting and now the return to permanent, as Mr Cool advised, should be enough.