The 17-year-old has been heavily linked with a move to England and other clubs across Europe since being promoted to Schalke's first team this season after nine years in the club's academy.
Ouedraogo contributed with nine goals and 12 assists in 23 matches at Under-17 level, before registering seven goals and two assists for Schalke's Under-19s side last season.
The 6ft 3in midfielder has since made 10 senior appearances in 2.Bundesliga this term and he became Schalke's youngest-ever goalscorer at the age of just 17 years and 80 days, surpassing the previous record set by Julian Draxler, when he netted on his professional debut in July.
Ouedraogo has been handed a start in seven of his 10 league appearances this season, while he has also represented Germany at Under-17s level on 15 occasions, including five outings at the European Championships earlier this summer.
The 2006-born prodigy is under contract at Schalke until the summer of 2027, but the German club may struggle to keep hold of the highly-rated youngster heading into the New Year.
According to Sky Deutschland reporter Florian Plettenberg, Ouedraogo will possess a release clause in his contract worth between €9m (£7.8m) and €12m (£10.5m) in 2024 if Schalke manage to qualify for European competition next season - their only route to European qualification is by winning the DFB-Pokal this season.
If Schalke fail to qualify for Europe - the most likely option - then Ouedraogo's release clause will be priced at just €7m (£6.1m) heading into next summer.
However, Plettenberg adds that the midfielder's release clause could rise to €20m (£17.4m) if he makes his senior debut for the German national team, now managed by Julian Nagelsmann.
Ouedraogo is believed to be one of a number of midfielder's on Man United's radar ahead of 2024, with manager Erik ten Hag said to have set his sights on bolstering his squad in January.
Liverpool are also understood to be exploring the possibility of strengthening their squad, with Jurgen Klopp potentially eyeing up a replacement for Thiago Alcantara who is out of contract next summer.
Chelsea, meanwhile, continue to scout the market for young talent despite forking out in excess of £250m on midfielders alone since the arrival of co-owner Todd Boehly.