Da Costa could be marking England Under-21 striker Andy Carroll, who was charged with assaulting an ex-girlfriend this week.
Newcastle skipper Kevin Nolan will return to the squad for the Premier League trip to West Ham.
The 28-year-old was rested for last weekend's 2-2 draw with Wigan as he battled a persistent ankle problem, but will be included this time around.
Danny Simpson could also travel after getting a third reserve team game under his belt following his return from a long-standing ankle problem, but Sol Campbell (thigh) will be missing once again.
Steven Taylor (shoulder) is due to return to training on Monday, while Steve Harper is around four weeks away from doing the same, but Leon Best (ankle), Hatem Ben Arfa (double leg fracture) and Dan Gosling (knee) are still out.
West Ham's Matthew Upson is pushing for a return to after missing last weekend's draw at Wolves with a neck strain.
Winger Pablo Barrera and defender Winston Reid are back in contention after being rested last week following their return from international duty.
Midfielders Thomas Hitzlsperger (thigh), Zavon Hines and Jack Collison (both knee) are long-term injury absentees.
WEST HAM (from): Green, Stech, Jacobsen, Spector, Upson, Gabbidon, Ben Haim, Reid, Tomkins, Da Costa, Ilunga, Parker, Dyer, Noble, Boa Morte, Behrami, Faubert, Kovac, Barrera, Piquionne, Cole, Obinna, McCarthy.
NEWCASTLE (from): Krul, Soderberg, R Taylor, Simpson, Perch, Ferguson, Enrique, Coloccini, Williamson, Kadar, Smith, Tiote, Barton, Routledge, Gutierrez, Guthrie, Vuckic, Tavernier, Donaldson, Nolan, Carroll, Ameobi, Lovenkrands, Ranger.