Although we do not know how reliable Peel's sources are, there is likely some credibility given his NHL involvement for over 20 years. Along with that, Oilers General Manager Ken Holland said in his press conference this afternoon "I believe in second chances" when asked about Kane.
TSN's Pierre LeBrun's belief is that any potential Kane signing won't take place until later this week. LeBrun spoke to Kane's agent, Dan Milstein, who is quoted as saying:
"We are interviewing with teams. Almost done. Contract by weekend.''
Based on this, it's safe to assume that Kane will have an NHL contract sooner rather than later. It could even be a done deal by tonight if Peel's sources are correct.