The 19 year old, who spent most of last season injured was expected to stay at Brentford and fight for his place if he was not offered a contract by Sheffield United but manager Neil Warnock was impressed with the young man,
"He's only a young lad and quite an exciting prospect" said the Blades boss.
"It's a shame" said Allen,
"We'd hoped he was going to stay with us and provide cover for our strikers, but when a big club comes calling he has every right to leave"
Brentford had offered the Aisian a three year deal but the Blades only offered a one year but on slightly less pay,
"We just felt he deserved the chance to show us what he can do this year. We'll see how he goes in the next few months and decide where to go from there."
The player is expected to accept the deal and move to the Blades in time for this weekend's opening round of Championship games.