The veteran striker, who turns 40 in July, scored the penalty which beat Watford in the Championship play-off final at Wembley to send the Eagles back into the top flight. Phillips is a free agent after spending the end of last season on loan at Selhurst Park from Blackpool.
"We are in conversations with them. The chairman and the manager have been away on holiday and it is only really in the last few days that we have made contact, but I spoke to the gaffer a couple of days after the play-off final and he made it clear that he wanted me to stay," Phillips told Sky Sports News.
"Hopefully we can get it sorted in the next week so that I can report back with the rest of the lads. It is an exciting season ahead and to be a part of that would be fantastic."
Palace have been linked with former West Brom winger Jerome Thomas, who is also a free agent, as well as Sunderland's Wales midfielder David Vaughan, goalkeeper Scott Carson and Bristol City winger Albert Adomah.