The two companies were in discussions to buy the division last year, but no deal was made as they couldn't agree on a price, sources have said.
It was unclear how far along the more recent talks were, or what prices were being considered.
An IBM spokesman said on Monday the company wouldn't comment on the report, nor on similar reports in other media outlets.
Bloomberg, citing a person with direct knowledge of the matter, said Lenovo was in serious discussions to buy the unit and that a deal may be signed within weeks. The Wall Street Journal, also citing unnamed sources, said Dell may be among the potential buyers, though it was unclear how serious Dell was.
Dell went private in a $25 billion deal last year, following prolonged troubles at the computer maker.
IBM's x86 server business sells servers used to power corporate data centers. Last year, Lenovo put the value of the division at below $2.5 billion, according to the Wall Street Journal.