A few days ago, I would have said the idea was extremely unlikely, on its face. After seeing the moon-buggy trailer, I think FD might well be seriously considering the idea...
It has been suggested before. To sum up my thoughts on Elite: Oh, No! The Giant Mechanical Chickens of Piratey Doom Are Here! Edition:
• A mech game is a Very Good Thing if they can do it well;
• Mech games are very difficult to get right - most attempts fail dismally, IMO;
• I backed and want ED, a space-ship game, rather than a mech game;
• If they do it, it might develop and play a lot easier as a separate thing, rather than an ED patch.
An actual MechWarrior license seems incredibly unlikely: the rights to faithfully combine ED with MW would involve some amount of negotiation* - and would require a significant effort to reconcile their very different storylines, histories and simulated technologies. It's not impossible (many aspects of ED - such as the attritionalised technological history and the heat mechanics - seem somewhat inspired by the other franchise), but it would be a substantial task. FD could just license the mechs and ignore the rest, but in that case, they might as well develop their own mechs from scratch.
It's worth noting that the larger mechs we're all thinking of are larger than the average ED spaceship. A Fafnir mech is apparently 100 tonnes, not counting weapons and ammo, looks to be about the size of three Asps glued together and doesn't look likely to fit in a standard Anaconda. Smaller, lighter mechs are more plausible.
*(For those wondering, MechWarrior (which is owned by Piranha Games) is based on BattleTech (which is owned by Topps), which incorporates components licensed from Macross (which is apparently owned by Japanese company Big West, with videogame rights currently held by Namco-Bandai Games), some of which are exclusively licensed in North America to Robotech-owner Harmony Gold (who seem to have a history of being uncooperative and litigious). The BattleTech, Macross and Robotech franchises presumably come with their own merchandising agreements with yet more third-parties, some of which are very likely to be exclusive and very probably vary from country to country, given how old the franchises are. I've no way to tell if any of BattleTech's or MechWarrior's previous developers or publishers have retained any partial rights to the franchises, or not. Just working out who definitely owns all the rights might be enough to cause FDs lawyers to literally melt from exhaustion. Actually getting hold of all the rights would probably need a ten-thousand-strong army of nuclear-powered cyborg clone lawyers, all bearing a suspicious resemblance to Fyvush Finkel.)