Alli was substituted on 81 minutes in the last-16 game against Colombia after he seemed to be struggling from a thigh problem that had kept him out of England's last two group games against Panama and Belgium.
Young, meanwhile, had been injury free in the tournament until he suffered an ankle injury in the last game.
Despite their knocks, both players were able to return to training with the squad at their training base in Repino on Thursday as the squad looks forward to their quarter final clash against Sweden on Saturday in Samara.
However, the outlook seems to be worse for Jamie Vardy. The Leicester striker suffered a groin strain in extra-time of the Colombia game, after coming on as a substitute in the second half of regular time, and it is unlikely that he will be fit in time for the match against the Swedes.
Gareth Southgate has put an emphasis on the importance of recovery in this period of the tournament, and believes that he has been proven correct in his decision to rest players against Belgium given that the Colombia game went to extra-time.
Various members of the squad suffered from cramp and minor knocks in a brutal battle on Tuesday, including Kyle Walker and Harry Kane, but all are thought to have recovered and will be avaliable for selection.