West Ham will take on Arsenal at the Boleyn Ground in the Premier League on Saturday afternoon.
Barnes believes that the Gunners will pick up all three points from the encounter courtesy of a 2-1 victory.
The former Celtic manager has also backed Alexis Sanchez and Danny Welbeck to score the goals for Arsenal.
“Spurs’ draw last week gives Arsenal some hope in the title race,” Barnes wrote on Titanbet.co.uk. “If they win their game in hand and keep up their current form they can close the gap between them and Spurs to one point, and Leicester are not far enough ahead of them to make it impossible.
“On that basis I think they’ll beat a good West Ham team. Goalscorers – Alexis Sanchez and Danny Welbeck.”
Slaven Bilic’s side are strong at home, and with France international attacking midfielder Dimitri Payet in red-hot form, they certainly have a good chance of winning this weekend.
Arsenal need to win against the Hammers in order to maintain their slim chance of winning the Premier League title this season, while West Ham are in the hunt for a top-four finish.