Two different concepts for a B757 successor emerged over the last few weeks.
First, there was an article by "The Motley Fool" (not exactly an aviation expert website) speculating about a B757MAX (and Scott Hamilton from Leeham Co. confirming these rumours), with composite wings and a new engine. Although this rumour was quickly dismissed by Steve Wilhelm from the Puget Sound Business Journal and another "Fool" and Boeing itself assured that they are not planning any B757MAX, it would be a relatively straigthforward and easy way to fight against the A321neo, as the numbers and the market already showed that the B737MAX-9 will be an inferior aircraft (I expect some announcements in the not too distant future that will further show that Boeing has a problem here). A new wing, new wingbox and new engines (which would be a few percentage points better in SFC than the PW1100G and the LEAP-1A) would provide enough improvement to be a very good aircraft for thin transatlantic routes. But then what? Airbus would not stand by and could develop a A322 with a similar fuselage length, also a new wing and wingbox and the same engines. And with successors for both of the narrowbody families planned for 2030+ that will likely start at today's B737-800 size, an EIS around 2022 would provide a production run of 10 years at best. So that concept does not really make sense.
Meanwhile also Scott Hamilton wrote another article about the subject, making clear that the "757 replacement" can only be part of a new family of aircraft, starting at the B737-800NG/B737MAX-8 size and topping at about 240 passengers, set by the aspirations from Airbus regarding the A321neo and that an EIS would be not anytime soon, i.e. not 2022.
The other concept emerged from an article by Aspire Aviation and this is completely different. Daniel Tsang proposes a small twin aisle family with a 2-3-2 seating configuration, comprising of two models between 200 and 240 seats. This of course would be a clean sheet design with the associated high development costs. The B737MAX family would still sell, he thinks, for shorter routes, as the "NSA" (New Small Airplane, not the other one...) would be optimised for routes around 4000nm in a 200-220 seat 2-class layout (where a B737MAX-9 and a A321neo would have to trade range versus payload).
But would the market be large enough for such an aircraft to justify a completely new aircraft, built from (today) very expensive carbon fibres? I think: yes and no! No, as I think the seat count of 200-240 would not cover a market potential large enough. And yes, if this NSA (albeit then not so "small") would occupy a larger part of the market, ranging from the B757-200 all the way up to the B767-300, say, from 220-280 passengers and a range around 4,500nm, to cover transatlantic flights between the US East Coast and Europe. This aircraft would have the potential to replace all the B757-200W, B767-300ER, A330-200/300 and maybe also some B787-8 that are used on these routes today (and more then).
Now: could this aircraft be the first Boeing to be powered by a geared engine?
A few weeks ago Rolls Royce very openly committed themselves to the geared technology and pursues such an engine for 2025. As I do not believe we would see the "NSA" (I would call it "NST", for "New Small Twin") before 2025, that could fit in Boeing's time planning.
Now with two of the big engine companies in the "geared camp" what will GE do? My bet: the next generation of narrowbody engines (beyond the A320neo/B737MAX generation) will be "geared only" - including GE! Of course nobody from GE (or Safran) will say so openly today, because that would mean to admit concede against the "gear". But I am sure that behind the scenes GE is working closely with their new affiliate Avio Aero in Italy (providing the Fan Drive Gear System for the PW1100G) to have a an engine architecture ready for the mid 2020's. And Snecma is working on a geared open rotor in the Clean Sky project.