The 39-year-old, who scored the winning goal for the Eagles in their Championship playoff final win over Watford last month, is currently a free agent after leaving Blackpool.
However, the veteran has claimed that he is in "conversations" with Palace as the club prepare for life in the Premier League.
"At the end of this week I will start ticking over and getting ready for pre-season, and hopefully that will be with Crystal Palace," he told Sky Sports News.
"We're 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.
"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."
Phillips turns 40 next month.