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"Marc would prefer to play again on Saturday, but he will need around four weeks," said Tuchel, whose side entertain Eintracht Frankfurt in the Bundesliga on Saturday.
Bartra, 26, underwent emergency surgery for a broken radius bone and to remove glass that became planted in his arm after the blasts shattered windows on the team's bus.
On Wednesday he said on Twitter that he was "doing much better" but he played no part in Dortmund's 3-2 defeat at home to Monaco in the first leg of their Champions League quarter-final.