Simpson, who has been training with the first team this season and travelled to Anfield for the Capital One Cup, has signed a new two-year deal with the club.
Whilst Whitfield, who is currently enjoying a positive loan spell with Kidderminster Harriers in the Vanarama National League, has agreed a one-year deal.
"I am delighted for Ben and Jack," commented under-21s manager Stephen Purches.
"They are both getting very valuable experiences at the moment in and around first team football.
"It is up to them now to make the most of this time and learn from the senior pros that they find themselves playing and training with.
"Knowing the attitudes of both players, I have no doubt that they will do that and begin to see the rewards of their hard work."
Subscribers can watch an exclusive interview with Simpson here
as he discusses his experience of travelling to Anfield with the first team.