Palace made an enquiry about the 25-year-old last season but are thought to have offered only around £75,000 for the player.
However, the Eagles' assistant boss Lennie Lawrence, who used to be director of football at Rovers, is known to be an admirer of Lines and a fresh approach is expected from the Championship outfit in the coming weeks.
However, despite their relegation to the fourth tier, Rovers are believed to be holding out for a six-figure fee for the midfielder.
The Bristolian has scored 21 goals in his 167 league appearances for Rovers since making his debut in 2006.
Lines is under contract at the Memorial Stadium until the summer of 2013.