I don't think there would be money to be made - that's the point. If there is not enough traffic for the Gatwick Express to continue to run a dedicated service into Central London (that is the airport traffic can be fitted on to the normal trains), I doubt there'd be enough transferring airport traffic to warrant a service. Plus there's the problem of the existing infrastructure.

There would be basically two ways there (building a line just for airport connection traffic is out of the question):
1 By building a connection from the airport southwards to the line at Ashford (Middlesex) then running south to near Weybridge, Guildford, Redhill and Gatwick. Unless another spur was built, the train would have to reverse at Redhill. Some of this track is heavily congested already.
2 By running via HEX tracks as far as Old Oak Common, then running south via Kensington Olympia and Clapham Junction. These trains could, I suppose, use the slots formerly used by Gatwick Express trains, but special trains would have to be built (again, out of the question economically) because the electrification systems are not the same on the HEX and South London lines.

I suppose 2 could work by diverting the new Heathrow stopping services away from Paddington so that after Ealing Broadway they served Olympia, Clapham Junction, East Croydon and Gatwick, also giving a direct rail service from these stops to Heathrow. But I still doubt anyone would invest in the rolling stock needed and would Gatwick/Heathrow passengers really want to take a stopping train via the London suburbs? Isn't a non-stop (well many stops, if you count being stuck on the M25) bus preferable?

PS Doesn't this really belong on the BMI board?

Edited to add: I think Swanhunter answered your question more succinctly while I was writing my long-winded post.