Roche's offer ran until last Friday but it has received shares worth only $4.55 million from the US company.
"All other terms and conditions of the offer remain unchanged," said Roche in a statement announcing it was extending the offer to March 23rd.
Roche said it had received some 102,165 shares at a proposed price of $44.50 a share.
The Swiss company said its price was 64 percent higher that Illumina's closing stock price on December 21, 2011 "the day before market rumours" about the potential bid drove Illumina's stock price significantly higher.
Illumina said: "The extension by Roche was expected."
"An extremely low number of shares have been tendered, consistent with our view -- and that of our stockholders -- that Roche's offer does not reflect Illumina's unique leadership position, business performance and future prospects."
Roche CEO Severin Schwan said however the Swiss giant continued to believe that the offer was "fair and comprehensive and provides a unique opportunity for Illumina shareholders."