The young Barcelona academy product, who has made eight starts in all competitions this season, is out of contract next summer but Barca want to tie him down for a further four years.
The central defender has already won two capps for Catalonia, but Barcelona are keen to loan him out to gain experience elsewhere.
Bartra is being considered as a potential long-term successor for 35-year-old Carles Puyol.
His loan availability has alerted West Ham and newly promoted Palace, who are both believed to be preparing offers. The centre-back, who came through the ranks at Barcelona before making his senior debut in 2009/10, is expected to feature for Spain's Under-21 side at next month's UEFA European Under-21 Championship in Israel.