Some considering has apparently been already done and has lead to the US Army’s CLAWS (Combat Lightweight Automatic Weapon System) and LDAM (Lightweight Dismounted Automatic Machinegun) project(s).
http://www.janes.com/article/.../us-...alibers‎
So it is possible that within say ten years two new conventional – brass, steel or aluminium cased - cartridges could be in widespread NATO/US use as successors for the 5.56x45 and 7.62x51.

The rationale for dumping the 5.56 can be summarised almost on a thumbnail. The 5.56 is over-powered for close-quarter use and less handy than SMGs firing pistol-power ammunition. A lightweight 5.56 projectile also looses velocity and hitting power rapidly: the energy of the heaviest 77-grain sharpshooter projectile falls by more than 10 percent within each 100m from muzzle to 600m. Effective range in a carbine or para-MG is 200-250m and in long barrel weapons 350-450m. The 5.56 is generally unsuitable for echelon deployment, suppression and harassing, and as the basis of a tracer round.

Calibre of any successor would be greater than 5.56, less than 7.62; mass of projectile greater than 5.56x45 less than 7.62x51 and of 7.62x35. When fired from an individual weapon in automatic mode such a successor round would be less controllable than 5.56 and also 7.62x35. However, automatic mode is most likely during assault, ambush and counter-ambush when rate of fire guided by adrenaline has more utility than precise accuracy.

A successor to the 5.56 round could readily exceed its hitting power, and at longer range also that of the standard 7.62x51. For example a 123 grain 6.5mm projectile started at 2,600fps has more energy beyond 600m than does NATO’s 147 grain 7.62 projectile started at 2,700fps. Assuming development of a companion LMG there would be little benefit in alternatively deploying a 7.62 MG such as the Mark 48 or M240 down to squad level. The 7.62x35 Blackout developed for hitting power out to about 400m is not a suitable round for a longer-ranged LMG, or a DM rifle.

In the same general timeframe as the 5.56 successor, the 7.62x51 round could be succeeded by another more powerful cartridge that can defeat body armour at longer range. Such a 7.62 successor might be a 7.62 magnum, 7.82 magnum or even an 8.59 cartridge with a projectile of 200-plus to about 300 grains. Much lighter and less demanding than the 700 grain 12.7x99 which also requires a HMG platform that is too bulky and heavy for ready use by footmobile infantry.

The detail on CLAWS and LDAM is brief and dates from November 2013. Have found nothing more recent. It will be interesting to see what – if anything – emerges.