The Spanish champion secured the arrival of Junior Firpo from Real Betis on Sunday in a deal that could be worth €30 million ($49 million).
Barca has spent upwards of €230 million ($376 million) on new players in 2019, with Antoine Griezmann, Frenkie de Jong, Neto and Emerson among those to arrive in the close season.
The clubs is reportedly in negotiations for the season-long loan of Paris Saint-Germain star Neymar, who is pushing to leave the Ligue 1 champion just two years on from his world-record move from Barca.
Such a deal, which would likely include an option to buy in 2020, would help Barca balance its spending while negating the need to sell several first-team players before the window closes on 2 September.
Bartomeu thinks more arrivals at Barca are certainly possible in the coming weeks.
"We have a stronger squad, with more potential," he said.
"There are still several weeks left for the market to close and we could have more incomings.
"We have an ambitious and incredible squad, led by the best player in the world and in history, Leo Messi."
Neymar watched on as PSG beat Rennes 2-1 in Shenzhen to win the Trophee des Champions for the seventh year in a row.
The Brazil international was dragged into medal celebrations by Marco Verratti and appeared in good spirits, despite PSG sporting director Leonardo confirming last month the player wants to leave.
There was then a moment of controversy when Kylian Mbappe, who scored PSG's first goal, appeared to push Neymar out of the way as the team celebrated with the trophy in front of photographers on the pitch.