Yes, but nobody reported that other than ISIS themselves on their propaganda accounts, and that's where he got that rumour from.
There is some tough fighting going in the West of Baghdad though, but I very much doubt they can advance into Baghdad. The reason ISIS is strong in those areas (Falluja, Jurf Al-Sakhar, ...) is because they controlled it long before the attack on Mosul, so their positions there are very fortified and hard to break, especially with the government reluctant to bomb heavily because of fear for civilians, so they have to rely pretty much totally on ground forces, which is not easy when the opposition is well-trained, fortified and well-equipped. When they (ISIS) go on the attack though the story is totally different.