Qualcomm hadn't commented on the report, but an FT companion piece cited insiders who claimed that the company would "prefer" to remain independent. This could be a hostile takeover attempt, to put it another way.
Broadcom also hasn't confirmed anything. However, there are hints that it could entertain a takeover. The company recently announced intentions to "redomicile" as a US-based company instead of Singapore. Many thought that was an attempt to grease the wheels for the much smaller acquisition of Brocade (by sidestepping fears about foreign takeovers), but it'd make more sense if Broadcom was using its legal relocation as a launching pad for larger moves.
There wouldn't be any mystery behind an acquisition, at any rate. Broadcom is well-known for its many mobile chips (you'll find some in the iPhone X, for example) and its telecom infrastructure, but it doesn't have much in the way of LTE and 5G chips. That's a big problem in a world where smartphones dominate and many future Internet of Things devices will have always-on cellular connections. If Broadcom snaps up Qualcomm, it'll be ready for whatever comes next -- and would virtually dominate the mobile chip space.