First-class average: 30.91
By the time he returned from England's tour to India at the end of 2016 with a finger injury, Hameed looked destined to replicate the smooth transition of Cook into Test cricket. It was not to be, though. He has averaged just 19.52 in first-class cricket in the subsequent couple of seasons without a single century. The 2018 season has been especially gruesome: he has averaged just 9.70 in the Championship and is currently unable to get into the Lancashire side.
First-class average: 43.92
As the first - and at present, only - man to have scored 1000 Championship runs in 2018, Burns has been knocking at the door hard all summer. He is, in some ways, similar to Cook: left-handed, not especially easy on the eye, but blessed with good judgement outside off stump and strong levels of concentration. He has now scored 1000 first-class runs in each of the last five seasons and has drawn praise from Dale Steyn among others. He also has the highest first-class average on this list. He can probably count himself most unfortunate if he does not win a place in the Sri Lanka tour party.
First-class average: 35.94
Long seen as one to look out for, Gubbins is another left-hander with some similarities to Andrew Strauss. He scored more than 1400 first-class runs as Middlesex won the Championship in 2016 but suffered a drop off in the form the following season. A particularly good player of fast bowling, he has a reputation of being uncomfortable against spin and endured a tough Lions tour to the Caribbean last winter. With winter tours to Sri Lanka and the Caribbean coming up, that may count against him.
First-class average: 39.21
When Duckett scored more than 2700 runs in all formats during the 2016 season, he was promoted to both the Test and ODI sides. But he found the step-up in class tougher than anticipated and, struggling against spin in particular, was dropped after four Tests produced an average of just 15.71. He has not found life easy since returning to the county game, either. He averaged 25.00 for Northants in Division Two cricket this season and, having just moved to Nottinghamshire, batted at No. 4 on debut. Not having the best disciplinary reputation - he was dropped from the Lions team after an incident in Perth during the Ashes - will do him few favours, too.
First-class average: 33.84
With a batting average of 22.65 after 11 Tests, Jennings can probably count himself somewhat fortunate to retain a place in the England side for the Oval Test. As the man in possession, though, he has a decent chance of retaining a spot on tour simply because the selectors may be reluctant to blood two new openers at the same time. His equable temperament has impressed the England management, but the lack of runs is becoming a serious problem.
First-class average: 34.91
Dropped by England only a few months ago, it seems too early for Stoneman to return. He has recently returned to county cricket - after some time away for personal reasons - with a century but, after averaging 27.68 in his 11 Tests, he may have to score heavily for some time to push for a recall.
First-class average: 36.65
It's nine years since Denly last played international cricket - and limited-overs international cricket, at that - and, at the end of 2014, when he was released by Middlesex, it seemed his career could be over. But, after a couple of good seasons in the county game, he is back in the mix. In some ways he fits the bill nicely: he is a right-handed batsman and decent legspinner. And, after four first-class centuries in 2017, he has managed three more this year. It would be a remarkable selection - Denly tends not to open any more - he has gone in at No. 3 and No. 4 in his last few games - and he plays in Division Two of the Championship, but it does seem it could happen.
First-class average: 37.81
Having given-up red-ball cricket for now, it seems unlikely Hales will be considered even though Adil Rashid has reversed his decision - in somewhat different circumstances, given the lack of spinners available - to return to the Test side this season.
First-class average: 37.72
There was definitely some interest from the England management in playing Roy in the Test side earlier this summer but, as he has not played a first-class game this year and plays in the middle-order for Surrey, he can probably not be considered a serious candidate.
First-class average: 40.72
As the only man on this list other than Burns with a first-class average of 40, Mitchell should be under consideration. It seems his age may count against him, though the example of Chris Rogers suggests it should not be the case. A compact right-hand batsman and good slip fielder, Mitchell has hit three Championship centuries in 2018 and only four men have more Division One runs this season.
George Dobell is a senior correspondent at ESPNcricinfo