The Newcastle United winger is the subject of Selhurst Park interest.
Townsend could be a Championship player next season
Townsend, who was cut from Roy Hodgson's preliminary England squad for Euro 2016, only arrived in the North East in January from Tottenham Hotspur.
Townsend (R) missed the 2014 World Cup through injury
Though he was unable to keep Newcastle in the Premier League, the 24-year-old caught the eye with four goals from 13 appearances.
Townsend scored for Newcastle against Palace last season
Townsend, though, is said to want more time to consider the move, reportedly informing Palace he is not yet ready to commit to a move.
And, in light of this, the Telegraph claims the Spurs product plans to use the rest of the month as thinking time.
A report in the Sun last week claimed Palace were hoping to offload midfielder Jordon Mutch to Norwich City in order to fund a move for the Newcastle man.
Mutch could be sold to raise funds, a report claims