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The 20-year-old only put pen to paper on a new deal with the club in March that takes him through to 2022, but Ole Gunnar Solskjaer's side have indicated their readiness to let him depart on a temporary basis.
And Baumann has reaffirmed his side's interest in Chong, insisting that discussions are underway with the Red Devils.
"He is a player who is interesting for us, no question about it," he told reporters."We need a player like him in the position he plays. We are in good talks with Manchester United, but there are several details to be agreed on."
"I like to keep a low profile when it comes to something like this, but when the player's advisor communicates so aggressively, there is no point in denying our interest."
Chong's agent Erkan Alkan previously confirmed that the player was keen on a moveto Germany's top-flight in search of further game-time, stating earlier this week:"Tahith wants to go to the Bundesliga."
Reports in Germanysuggest that Chong may sign a two-year loan contract with Werder, though it is believed that the Bundesliga club will not have a purchase option in any deal.
If Chong does not depart immediately, he may yet play a part in United's Europa League campaignafter the club sealed their place in the quarter-finals in Germany next week.
The winger came off the bench in a 2-1 victory over LASK to help seal his side's berth in the last eight following a convincing 5-0 victory in the return fixture earlier this year.
United face Copenhagen next, with victory potentially setting up anall-English encounter with Wolves, as Solskjaer looks to claim the first trophy of his tenure in charge at Old Trafford.