For large parts of the season, Arsenal have been within touching distance of the top of the Premier League table, but in recent weeks, they have slipped off the pace and also suffered a costly defeat to Barcelona in the Champions League.
Their slump has led to suggestions that they must strengthen when the transfer window reopens in the summer if they are to compete in all competitions, rather than just in the FA Cup which they have won in the last two years.
McCoy said: "I'd like to sign Everton's middle - Stones, Barkley and Lukaku.
"I think that Barkley has loads of presence, big physical man, can play football. Stones looks like he is a good footballing defender.
"I think Lukaku, at 22 as well, would make Arsenal a Premier League winning team. We definitely need a physical presence in midfield. We haven't had one since Patrick Vieira."
Stones has attracted interest from Chelsea, Manchester City and Barcelona over the last 12 months, but the level of his performances have dropped in recent months.
Barkley and Lukaku have scored 35 goals between them this season, and it would take an extravagant bid for Everton to be tempted into a sale.