According to F-15 EAGLE Origins and Development 1964 - 1972 by Jacob Neufeld Boeing was one of three contractors awarded concept formulation studies for FX in March 1966 (others were North American Aviation and Lockheed - Grumman participated at its own expense).
On 11 August 1967 the USAF sent requests for a second round of studies to 7 companies. General Dynamics and McDonnell-Douglas won contracts, Grumman, Fairchild-Hiller and North American Aviation all participated without funding at company expense. This leaves 2 companies which either didn't bid or didn't win contracts and refused to fund their own studies - Boeing is likely to be one.
May 1968 – concept definition agreed. RFP for FX contract definition issued to McDonnell-Douglas, North American, Grumman, General Dynamics, Lockheed, LTV, Fairchild-Hiller, Boeing.
August 1968 – Only 4 serious bids were received; North American (NR-335), McDonnell-Douglas (Model 199B), Fairchild-Hiller and General Dynamics.
I don't know anything specific about the Boeing FX studies of 1966, though Neufeld mentions that contractors in general favoured podded engine designs.
