Carroll is set for a long spell on the sidelines following ankle surgery and with big-money signing Enner Valencia also set to miss the start of the season the Upton Park club are short of options in attack.
Wickham, an England Under-21 international, made a big impression during two loan spells last season at Sheffield Wednesday and Leeds United.
He returned to the North-East club and made his mark in the Premier League, netting five times in the last six matches of the season to help save the Black Cats from relegation.
It is unlikely that Sunderland would let him go as he is just beginning to fulfil his potential and to justify the £8 million the club paid for him in 2011.
The 21-year-old's contract situation could open the door for West Ham to swoop in, however, with his future at Sunderland in doubt.
Poyet has made it clear that if a long-term contract cannot be worked out he may be forced to sell the striker.
"For me, Connor’s situation is clear," the Uruguayan said. "He needs to sign a new contract or we let him go – we sell him. There is nothing in between."