Roche said it had made "multiple efforts" to start talks with Illumina to negotiate a deal but the US firm had not been willing to enter "substantive discussions"
"Roche has therefore decided to promptly commence a tender offer to purchase all of the outstanding shares of common stock of Illumina for $44.50 per share in cash," said a company statement.
This offer was "full and fair value" for the company, Roche chief executive Severin Schwan said in a statement.
He added: "It is our strong preference to enter into a negotiated transaction with Illumina, and we remain willing to engage in a constructive dialogue with Illumina to jointly develop an optimal strategy for maximizing the value of our combined business."
The statement said the offer represented a 64 percent premium over Illuminas stock price on December 21st, 2011 and put the value of the San Diego-based company at $5.7 billion.
A brief statement from Illumina acknowledged that Roche had made an "unsolicited offer" for the company.
It said the board of directors would "thoroughly review" the proposal and make a recommendation "in due course" adding that it had asked share holders to take no action in the meantime.