The 18-year-old Sporting Lisbon starlet is widely regarded as one of the most talented young players in Europe, and Manchester City had a £2m bid for him rejected last year.
The teenage winger was even a target for City before he signed his first professional contract with Sporting in 2010, and they then had a £2m bid turned down last October.
But reports in Portugal now claim Bruma is wanted by Bayern Munich. And he could be on the move sooner rather than later after he decided against a contract renewal with Sporting.
His current deal expires at the end of the 2013-14 season. The Portugal under-19 international was also thought to be a target for Chelsea.
The report claims City may hope that it will be third time lucky this summer and make another offer for Bruma, with Chelsea waiting in the wings.
But both could ultimately miss out as Bayern Munich are reportedly ready to make a £4m move for the forward. Sporting are struggling financially and the offer could be enough to persuade them to part with their star academy product.
Chelsea and Manchester City are looking to put a greater emphasis on youth development. The Blues have won two of the past three FA Youth Cups, while Manchester City have pledged to build a new £200m training and academy facility next to the Etihad Stadium.