The short answer is, no. Not with the naked eye at least, but if you use a highly potent set of binoculars or a telescope, this is indeed possible.
There are a number of accounts, some dating back from ancient times, that tell of how star gazing is possible during the daytime. Various old wives’ tales speak of the possibility of seeing stars during the daytime from the vantage point of the bottom of tall chimneys, coal pits or cisterns. Of course, this doesn’t work.
People reasoned that because of smaller visual angle and the greater contrast one gets from gazing at the sky bottom-up from a chimney, for instance, stars become visible. One of history’s greatest naturalist, Alexander von Humboldt, actually tested this theory during an experiment, joined by his students, in the XIXth century. At the time, the team chose an ideal 230-foot chimney with a 16-foot opening, and even waited for Vega, the fifth brightest star in the night sky, to pass over them to increase their chances of success. They failed miserably.
It’s not that they didn’t tried hard enough, it’s just that the naked eye can’t discern the light emanating from stars during daytime. The light emanating from distant stars is just as intense during the day and the night, but it all falls down to contrast. The sun shines 550,000 times brighter than the nearest brightest object – the full moon – and as such, the intensity of stars is far too low to be visible.
If you use a telescope, however, that’s another matter. If you’re interested, this website offers some great insight into how to maximize your daytime telescope observations.