The 20-year-old goalkeeper has been offered a new deal following a string of fine performances for Orient, which included penalty shoot-out heroics on his debut in the Capital One Cup victory against Charlton.
Allsop joined on a six-month deal in the summer, having been released by Millwall.
With fellow goalkeepers Jamie Jones and Lee Butcher suffering injury problems, Allsop has since cemented his place in the side and Slade believes the time is right for the former West Brom trainee to pledge his future to the club.
Slade told London 24: "It would be foolish of us not to keep him and foolish of him not to sign because he is getting games and he is playing week in and week out at this moment in time and he couldn't have dreamed about that four or five months ago.
"He is on a short-term deal at the minute and we have already put an offer to him and talks are on-going."