The veteran pair are set to be released by Everton this summer.
The Blues pair are out of contract in the summer and were named on the list of players that would be leaving the club.
However, that does not necessarily mean they will be departing Goodison Park as new deals could be offered to extend their stay beyond this year.
Both players want to hold talks with new Everton manager Ronald Koeman before making a decision about their futures.
They are both naturally keen to stay at the club having spent their careers there after breaking through the youth ranks.
Those talks are yet to happen though according to the Liverpool Echo, with it unknown whether the Dutchman sees them as part of his plans.
Given that both players are now 35, it would be surprising if either were handed a new deal at this stage. The Blues are expected to be busy this summer with reports indicating that Koeman will be strongly backed by Farhad Moshiri.
If that is the case, then signing replacements rather than handing Osman and Hibbert new deals looks the more likely choice.