The academy graduate has spent the last two seasons on loan at Vitesse and Southampton, contributing a total of 20 goals from 73 appearances in all competitions.
Broja's performances for the latter in the Premier League have increased expectations among the Chelsea fanbase that he can eventually establish himself as a long-term option down the middle of the team's attack.
However, his imposing and swashbuckling style of play has also led to widespread interest in his signature from clubs in England's top flight and on the continent.
If reports are to be believed, Chelsea have already received contact from various teams this summer, giving Tuchel and the club's owners with plenty to ponder.
Nevertheless, Tuchel has always said that he wants to see how the Albania international fares in pre-season, a stance which has seemingly not changed.
Ahead of Chelsea's friendly with Club America this weekend, Tuchel told reporters: "Armando is our player first of all and we have, at the moment, no interest in selling him. He is here to make an impression after he was on loan in Southampton.
"That's his situation from where we look up front. It's good if there's interest as it shows us there's talent and potential. It shows us that Armando is in the position to impress and become a Chelsea player.
"When will he become a Chelsea player? Nobody knows but hopefully as soon as possible. He got injured and there's a delay for him, which is never nice because a young player should normally make an impression from the first minute in pre-season. Now we have a bit of a delay in that but that's the situation."
Earlier in his press conference, Tuchel had revealed that the 20-year-old had "landed in a funny way on his ankle and Achilles", but insisted that the prospect had avoided suffering a serious injury.
West Ham United have previously been tipped to emerge as the favourites to sign Broja with the Hammers allegedly offering in excess of £25m to bring in competition for Michail Antonio.
Everton manager Frank Lampard has also been credited with an interest in Broja having given the player his Premier League debut during his time at Stamford Bridge.
Serie A giants Napoli, who need to replace the likes of Lorenzo Insigne and Dries Mertens, are another club who are said to be monitoring the situation.
While speculation persists regarding incomings and outgoings at the West Londoners, Chelsea officially announced on Saturday morning that they had completed the signing of Napoli centre-back Kalidou Koulibaly.