Gayle rejected the chance to join Bristol City last summer and has been linked with a move away on a number of occasions since.
It is thought Palace remain open to a sale and now relegated Newcastle have been credited with an interest.
A bid of £10million may be enough to convince the Eagles to cash in on the 25-year-old but it remains to be seen as to whether Gayle will be prepared to drop down to the Championship.
Newcastle’s confirmed pre-season fixtures:
Bohemians vs Newcastle United - Saturday, July 16 (2pm kick-off)
Doncaster Rovers vs Newcastle United - Wednesday, July 20 (7.45pm)
KSC Lokeren vs Newcastle United - Saturday, July 23 (4.30pm)
Newcastle United vs Vitesse Arnhem - Saturday, July 30 (3pm)
AUGUST
Friday 5: Fulham (a) (7.45pm)
Saturday 13: Huddersfield Town (h) (3pm)
Wednesday 17: Reading (h) (7.45pm)
Saturday 20: Bristol City (a) (3pm)
Saturday 27: Brighton (h) (3pm)
SEPTEMBER
Saturday 10: Derby County (a) (3pm)
Tuesday 13: Queens Park Rangers (a) (7.45pm)
Saturday 17: Wolves (h) (3pm)
Saturday 24: Aston Villa (a) (3pm)
Wednesday 28: Norwich City (h) (7.45pm)
OCTOBER
Saturday 1: Rotherham United (a) (3pm)
Saturday 15: Brentford (h) (3pm)
Tuesday 18: Barnsley (a) (7.45pm)
Saturday 22: Ipswich Town (h) (3pm)
Saturday 29: Preston North End (a) (3pm)
NOVEMBER
Saturday 5: Cardiff City (h) (3pm)
Saturday 19: Leeds United (a) (3pm)
Saturday 26: Blackburn Rovers (h) (3pm)
DECEMBER
Saturday 3: Nottingham Forest (a) (3pm)
Saturday 10: Birmingham City (h) (3pm)
Tuesday 13: Wigan Athletic (a) (7.45pm)
Saturday 17: Burton Albion (a) (3pm)
Monday 26: Sheffield Wednesday (h) (3pm)
Saturday 31: Nottingham Forest (h) (3pm)
JANUARY
Monday 2: Blackburn Rovers (a) (3pm)
Saturday 14: Brentford (a) (3pm)
Saturday 21: Rotherham United (h) (3pm)
Saturday 28: Brighton (a) (3pm)
FEBRUARY
Wednesday 1: Queens Park Rangers (h) (7.45pm)
Saturday 4: Derby County (h) (3pm)
Saturday 11: Wolves (a) (3pm)
Tuesday 14: Norwich City (a) (7.45pm)
Saturday 18: Aston Villa (h) (3pm)
Saturday 25: Bristol City (h) (3pm)
MARCH
Saturday 4: Huddersfield Town (a) (3pm)
Tuesday 7: Reading (a) (8pm)
Saturday 11: Fulham (h) (3pm)
Saturday 18: Birmingham City (a) (3pm)
APRIL
Saturday 1: Wigan Athletic (h) (3pm)
Wednesday 5: Burton Albion (h) (7.45pm)
Saturday 8: Sheffield Wednesday (a) (3pm)
Saturday 15: Leeds United (h) (3pm)
Monday 17: Ipswich Town (a) (3pm)
Saturday 22: Preston North End (h) (3pm)
Saturday 29: Cardiff City (a) (3pm)
MAY
Sunday 7: Barnsley (h) (12pm)