The New York Times reported on Friday that Ballmer and Bostock had met, citing a person briefed on the meeting.
Its report followed that of gossip blog Valleywag, which said the two were spotted in Manhattan's Time Warner Center last Thursday.
Ballmer and Bostock's meeting is believed to be the second high-level contact between executives at the two companies in recent days.
Carol Bartz, Yahoo!'s new chief executive, told employees last week that she had an informal phone conversation with Ballmer after she was appointed leader.
Ballmer has repeatedly said that Microsoft remains interested in forming a web search partnership with Yahoo!, but that the software giant is keen to reach an agreement sooner rather than later.
Bartz has reportedly told colleagues that her "gut" instinct is to hold on to Yahoo!'s search business. However, she said that she would spend time studying the matter.
Microsoft proposed to buy Yahoo!'s search assets after the internet firm rejected its $44.6bn (£30.4bn) takeover offer last year.