Villas-Boas' plans for the season were dealt a major blow on Thursday when Younes Kaboul was ruled out for between three and four months after undergoing knee surgery.
When asked whether he would consider a bid for Dawson, Villas-Boas replied: "I don't think so.
"We have known about this possibility (that Kaboul would be ruled out) for quite some time. It was even in the discussions I had with Michael.
"At the moment that leaves us with four (fit) central defenders, so we are happy with the situation as it stands.
"It is a massive blow to lose Younes."