The NYT published a story Sunday alleging the Microsoft chief had on at least two occasions -- and possibly more -- asked a couple of women who technically worked for him out on dates, but apparently wasn't all that pushy ... and ultimately failed in both instances.

Bill is described as once attending a presentation in 2006 held by a female Microsoft employee -- who must've left quite an impression ... because it's alleged, based on NYT sources familiar with the matter, that he emailed her right after to ask her to dinner.

He allegedly followed up with this, "If this makes you uncomfortable, pretend it never happened." Turns out, the woman did exactly that ... ghosting him and never responding.

There's another alleged incident the Times describes, in which Bill traveled to NYC with a woman who worked for the Bill and Melinda Gates Foundation ... where the two of them attended a cocktail party. The woman claims Bill lowered his voice and said, "I want to see you. Will you have dinner with me?" She says she laughed it off to avoid answering.

The Times -- citing current/former Gates employees -- goes on to describe general clumsy approaches toward women at work overtime, at times making people a little uncomfortable ... but noting he never seemed predatory with his advances, or abused his power.

On the flip side ... WSJ has its own report, claiming Bill was essentially forced to step down from Microsoft's board in recent years because of an extramarital relationship that came to light with a Microsoft engineer, who claimed to have hooked up with Bill for years.