The duo have been the subject of two bids from former boss David Moyes, both of which have been rejected by the Toffees.
With time running out in the transfer window, the Red Devils have been linked with a return bid for at least one of the pair.
When asked if he is worried about the duo's future, Osman told BBC Sport: "Of course. We have got some top class players that we are desperate to keep hold of and the next 48 hours will tell us whether we can do that. From our point of view we want the window shut as soon possible."
The Toffees drew their latest Premier League game against Cardiff City to earn their third point of the season.