The 23-year-old, whose real name is Daniel Needs, made headlines last month when he spent seven days underground holding up work on the A30 road near Honiton, Devon.
Protesters at Manchester Airport claim to have already dug between three and four tunnels in woodland at the end of the existing runway, two of which have activists sleeping in them. They hope to delay and even prevent the proposed pounds 172m second runway, although details of the fortified tunnels already built are being kept secret for tactical reasons.
Melanie, 27, a demonstrator from Manchester, said: "We have heard Swampy is on his way. We are looking forward to his support. Obviously he has experience which can help us and it will help with the publicity because he is already so famous."
About 40 people are taking part in the protest, which is continuing despite warnings by police that methane in the ground is putting the demonstrators' lives at risk. A spokesman for Manchester Airport declined to comment.
Meanwhile, the former Beirut hostage Terry Waite gave the anti-runway protesters a boost by offering his support for their cause.
Mr Waite, who was born in nearby Styal, visited the demonstrators' camp and signed a green- skies document protesting about the environmental impact of the air-transport industry.
But Mr Waite refused to back illegal tactics adopted by some environmental protesters. "These people are taking direct action and have the support of some very respectable groups and associations," he said.
"I myself would not break the law. I would not do that. That is down to the individual conscience." Mr Waite gave evidence at the 101-day public inquiry 18 months ago opposing the runway but the inspector ruled against the protesters.