Stewart suffered a partial tear in his Achilles and is expected to be out for around four months leaving the Black Cats with just Leeds loan striker as their only senior first-team striker.
Simms went back to Everton from a loan spell with Sunderland in early January, but has only played a handful of minutes with the Goodison club since his return.
The 22-year-old scored seven goals in 17 games for Sunderland during his loan spell, and The Northern Echo reports that a return could be back on the cards.
However, the recall will very much hinge on what business Everton can do in the transfer window with strikers high on their priority list.
Sunderland have already signed Joe Anderson from Everton on transfer deadline day who follows Pierre Ekwah, Isaac Lihadji and Gelhardt as January window captures for the Championship play-off hopefuls.
READ MORE: Sunderland sign Everton U23s defender Joe Anderson as club strengthen ahead of play-off push