The Mirror says England international striker Carroll has yet to play for the Hammers under new manager Pellegrini, after damaging an ankle in pre-season. The problem needed surgery, which has kept him out until now.
The 29-year-old played 45 minutes of a friendly played behind-closed-doors against Brentford last Thursday and did not report any issues afterwards.
Providing there are no further setbacks in the coming days, he is likely to be named among the subs for Saturday's visit of table-topper City.
Midfielder Wilshere, who last played on September 1, has also undergone ankle operation.
The 26-year-old former Arsenal and England star has stepped up his recovery and there is a chance he'll make the bench against City.