Burnley are open to selling the player after they were relegated from the Premier League at the end of last season.
McNeil is also keen on continuing in the Premier League and is not keen on playing in the Championship in the 2022/23 campaign.
West Ham are interested in signing a player who could be available for a cut-price fee of £15m in the ongoing transfer window.
It has been claimed a move for McNeil could become a priority for West Ham if they fail to land Lingard this summer.
The Hammers have tabled a contract offer to the 29-year-old but he is believed to be inclining towards a move to Nottingham Forest, where he could earn £200,000 per week.
Nottingham Forest have offered more lucrative terms and West Ham are not willing to break their wage structure for Lingard.
A decision has not been made by Lingard and he is likely to make a decision over his future this week.
If he, as anticipated, opts for Forest, West Ham are likely to step up on their efforts to land McNeil in the ongoing transfer window.
The Hammers are likely to face competition from Crystal Palace, who have been interested in the winger since last summer.
