The German veteran is recovering from back surgery and Sport says he will be encouraged by Barca management to find himself a new club in January.
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The 33 year-old attracted an approach from AS Monaco last summer, which remain interested.
However, there is also the Premier League option, with Newcastle, Tottenham and Manchester United having already registered their interest with Barca.
Ter Stegen's deal runs to 2028, though Barca are prepared to release the veteran on a free transfer.
Instead, the three English clubs have suggested a loan-to-buy arrangement in January.