"Illumina would be an interesting business to acquire for Roche, but it is not essential to its development," the unnamed source told the paper.
The Basel-based giant launched its bid -- previously estimated at $5.7 billion -- for Illumina on January 25th.
But the US provider of integrated systems for DNA sequencing, had opposed the hostile move saying Roche's offer price was too low.
On Thursday, Roche increased its offer price by 15 percent but it is not clear if the sweetened proposal will persuade Illumina's leadership to back the takeover.
According to SonnatgsZeitung, Roche will not increase its offer again.
"The adverse party (Illumina) can be assured that Roche will not continue this game for long," the paper quoted another source as saying.