The Lions are 13thin the Kingstone Press Championship table and have the same number of points as 12th-placed York.
Swinton coach Gary Chambers said: “This is a massive game for us. There are no ifs or buts anymore; it’s about who’s more desperate on the day and who wants it most.
“We’ve shown we can compete with the top teams, and York have done the same as well.
“Now it’s down to desperation, but also smartness and who can do the little things when they’re needed.”
Knights coach Gary Thornton said: “We need to get a win as quickly as we can.
“These next two games are ‘must-win’. We’re getting perilously close now.”