Officials are likely to approve the deal without forcing Microsoft to sell any of its assets, Reuters reported.
But the deal still faces major hurdles even if it wins approval in Europe, with the UK’s Competition and Markets Authority (CMA) and the US Federal Trade Commission (FTC) both launching investigations into the takeover.
The CMA has already indicated that it believes the deal will hurt gamers, and suggested in recent statements that it was unlikely to approve the deal without at least some new restrictions.
Microsoft is buying Activision with the aim of integrating it with its Xbox business, and to boost the Game Pass subscription service.
But critics including PlayStation have said that the scale of Call of Duty is such that the purchase would make the gaming market unfair, since the size and pull of the newly merged company would be too large for it to be able to compete.
Some had suggested that the company might be required to get rid of some parts of the company it buys, such as the Call of Duty games, to ensure that competition in gaming stayed fair.
Microsoft has said that it will consider other options – such as licensing games to its rivals, so that Call of Duty is not exclusively available on the Xbox, for instance. Microsoft has suggested that it would commit to make the games available on the PlayStation and other platforms for a certain amount of time, for instance.
EU regulators are likely to be satisfied with such a licensing deal, Reuters said, citing three people familiar with the matter.