McLeish resigned from Birmingham City on Sunday and Villa made their move for the Scot barely 24 hours later.
Taylor said: "I think Alex has the strength of character but it won't be easy for him. He has a hardness about him.
"It would be difficult though, because many Villa fans would not want a Birmingham man as their manager and many Birmingham supporters might see him as a traitor. He is a strong man though, and I think he could cope with that."
Within 24 hours of McLeish's announcement, nearly 6,000 people signed up to a Facebook page entitled 'Aston Villa Supporters - We don't want Alex McLeish'.