Bale's future is a source of constant speculation, with United among those clubs regularly linked to signing the Real Madrid forward.
But former United striker Andrew Cole believes that Ole Gunnar Solskjaer's side need to be playing on European football's biggest stage to harbour hopes of recruiting world-class talent.
Asked if the club should make a move for Bale, Cole said: "I think Manchester United should be going for all top players of that calibre. That's what Manchester United is about.
"Do those players want to come to Manchester United? That's the question. If Manchester United miss out on Champions League football top players want to play Champions League football.
"When you are playing at that elite level, it's not all about money. People think it's all about money, but you speak to players at elite level.
"Do you want to play Champions League football or do you want a few more quid? They will say Champions League, because they want to win it - it's a special competition.
"So if Manchester United miss out on Champions League football, it becomes difficult for them to attract players. It can be tough."