The England international striker is due to hold talks over a five-year contract at Upton Park with Hammers boss Sam Allardyce next week, after the club reportedly agreed an initial £16m fee with Liverpool.
Allardyce has made signing Carroll his top priority this summer and according to The Sun co-owner David Sullivan has backed his manager, agreeing to pay Carroll a club-high wage of £100,000 per week.
Carroll's deal will be worth a reported £25m in wages across his five-year deal, with Liverpool due a further £3m in add-ons based on performances, taking the total outlay for any potential move to around £44m.
The 24-year-old is yet to give the green light to any permanent West Ham deal, but a return to Anfield looks increasingly unlikely after Liverpool agreed a deal with Spanish striker Iago Aspas this week.
Carroll scored seven goals in 26 appearances during a productive loan spell in East London last season.