Bangladesh, who tasted their first ever series victory against Zimbabwe in January, will play two tests and also take part in a triangular one-day series also involving world champions Australia.
"I know the team's potential, it's just a question of turning the magic key and unlocking it," Whatmore told Reuters on Sunday.
"I know there are at least two players in our team who are going to become household names throughout the world.
"I don't want to name names because that would be putting pressure on them, but we are in the process of building stars for the future and we have a lot of talent," he added.
Whatmore, who guided Sri Lanka to World Cup victory in 1996, accepts conditions in England during May and June will suit the home side and that Bangladesh will have to raise their game.
"Wicket and climatic conditions will be completely different," he said. "Plus England are now the second-ranked test side in the world."
Bangladesh will start the series as clear underdogs, having lost 31 out of 36 tests since their debut in 2000, with just one win and four draws.
They have won nine of their 106 one-day internationals, including a victory over Pakistan in the 1999 World Cup.
SELF-BELIEF VITAL
Self-belief, Whatmore added, would be vital against England.
"I have to remind them that it's a level playing field, that the England players also bleed red blood, that they have two arms and legs just like us because sub-continental teams have struggled for a long time with that belief," he said.
Bangladesh have included three uncapped players in their 16-man tour squad -- wicketkeeper Mushfiqur Rahim, who averages 50 in first-class cricket, left-handed batsman Shahriar Nafees Ahmed and pace bowler Shahadat Hossain.
Among the established players most likely to shine against England are fast bowler Mashrafe Mortaza and left-arm spinner Enamul Haque junior.
Mortaza, without first-class experience when he made his test debut against Zimbabwe aged 18 in 2001, spearheads the Bangladesh attack and is capable of delivering the ball at just under 90 miles an hour (145 kph).
The 21-year-old, who has been advised by Australia speedster Brett Lee, took a career-best haul of four for 60 in the second test against England in Chittagong in 2003, including the key wickets of Michael Vaughan, Nasser Hussain and Graham Thorpe.
Haque junior, 18, was an instrumental figure in Bangladesh's breakthrough test win against Zimbabwe in January this year, taking six for 45 as the Asian team completed a crushing 226-run victory.
Although the second and final test was drawn, he returned match figures of 12-200 -- including a career-best return of seven for 95 in the first innings -- and ended the series as the highest wicket-taker with 18 at an average of 16.66.
Bangladesh start their England tour on Tuesday with a three-day match against British Universities at Fenners.
