That is likely to pressure United into selling De Gea if they do get a sufficient offer from either, and the club has made contingency plans in case that happens.
They are aware of Jan Oblak's interest and rate him highly, but sources see it as unlikely the club would pay so much for a goalkeeper in this window, as they prioritise other areas in an overhaul.
The Slovenian would cost around £100m.
Onana - who would be available at around £40m - is United's first choice, although Barcelona's Jasper Cillesen has also been made available to them.
Meanwhile, Paris Saint-Germain have moved ahead in the battle to sign Onana's Ajax teammate Matthijs De Ligt.
Barcelona have been the 19-year-old’s preference in terms of pure football, and United were willing to offer the highest wage with a deal of £350,000 a week, but sources say the French champions have gone higher as regards the latter.
PSG have also set out a persuasive plan, that explains De Ligt’s role in the team and future.
Barca have not yet given up hope, but it is felt by those close to the situation that the French club are now leading the race.
Join our new commenting forum
Join thought-provoking conversations, follow other Independent readers and see their replies