"It's going to take some time," Shanahan said.
The 49ers are also discussing the possibility of placing Armstead on injured reserve.
During Sunday's loss, Aaron Lynch stepped in for Armstead but suffered his own injury – a calf strain – during the game. Lynch is week to week.
Armstead was the 17th-overall selection by the 49ers in the 2015 NFL Draft. He has started all six games this season and had 16 total tackles, 1.5 sacks, and a pass defensed. Over his three seasons with the 49ers, Armstead has 50 total tackles, six sacks, and a pass defensed.
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