Not right now, no. There is a theory from the 1970s which suggested that there could be an ice age headed our way in the next few thousand years, or sooner -, but that theory is no longer accepted. Even without global warming, the next ice age is expected to be 50,000 years into the future. An Exceptionally Long Interglacial Ahead? There’s an idea that we might go into a mini ice age for 30 years as a result of the sun becoming a bit cooler than usual, but that’s just a small drop in temperature and it’s a prediction, not yet confirmed. In detail:

The 1970s theory was simply based on looking at the duration of previous interglacials, which usually last for 10,000 years. They just assumed ours would be the same duration as the previous ones. If so, with the last glacial period (popularly called an “ice age”) 12,000 years ago, then you’d think we are long overdue a new one. And that’s how they reasoned back then, see The Future of the World's Climate.

However back then they didn’t have any detailed theory, as the theory of Milankovitch cycles which is now accepted widely was only finally established as valid in the late 1970s through study of ice cores (though first put forward as a theory in the 1920s). The ice ages depend on interaction of many different cycles involving slight variations in the Earth’s tilt, how circular the orbit is (eccentricity) and the precession of the equinoxes. See Milankovitch Cycles and Glaciation

As a result, nowadays, based on a much better understanding of how it works, the scientists predict that ours would be a longer duration interglacial even without global warming, lasting about 50,000 years.

Then, there’s new research that suggests that the next ice age could be postponed from 50,000 to 100,000 years in the future due to the effects of the CO2. See: Fossil fuel burning 'postponing next ice age You can click through the link in that article to get to the nature paper itself complete under their sharing initiative.

In that paper, they say

" Using an ensemble of simulations generated by an Earth system model of intermediate complexity constrained by palaeoclimatic data, we suggest that glacial inception was narrowly missed before the beginning of the Industrial Revolution. The missed inception can be accounted for by the combined effect of relatively high late-Holocene CO2 concentrations and the low orbital eccentricity of the Earth7. Additionally, our analysis suggests that even in the absence of human perturbations no substantial build-up of ice sheets would occur within the next several thousand years and that the current interglacial would probably last for another 50,000 years."

So in other words yes, we were due to go into an ice age around the start of the industrial Revolution, but it's not just the CO2 that stopped it. The various cycles are complex with many factors interacting and their analysis suggests that this time around the interglacial would have lasted 50,000 years anyway.

Their crucial graph is this one on page 203 of the paper. The graph at the top shows the effects of different levels of CO2 now over the next 100,000 years. Notice that there's a significant difference between them, depending on the levels we reach in the near future, even 100,000 years from now. There is much less CO2 of course 100,000 years in the future, but you still see differences because the amount you have then if we get to 1000 gigatons this century is still double the amount you get if we don't go above 500 gigatons. Apparently even that small amount of CO2 is enough to be significant

Then there's another very different idea of a "mini ice age" which is what professor Zharkova predicts if I understand it right. That's similar to the Maunder Minimum when there were no sunspots and the sun was a bit cooler than usual with the Thames freezing over in London. It’s just a prediction and hypothesis, she’s not saying that the sun has started to cool down yet.

If we do get a mini ice age of that type - which depends on the sun not on Earth, then the global warming that we've had would offset it. But it''s quite a small effect, they say a reduction of average temperatures by 0.1 C, small compared with the global warming of 1 C. Of course local effects could be more than that, that's global average. Still, don’t expect ice sheets to start advancing. With all the CO2 in the atmosphere, it’s more like a short period of 30 years when maybe the Earth doesn’t warm up quite as much as it would otherwise.

You can read what Zharkova herself says about her theory and it’s relevance to climate change here: Is a Mini Ice Age Coming? 'Maunder Minimum' Spurs Controversy

See also There Probably Won't Be A “Mini Ice Age” In 15 Years