Everton have been linked with the former Valencia schemer this summer.
Everton are reportedly weighing up a big-money bid for the Spanish schemer who would likely become the Toffees' all-time record transfer, should a move materialise.
ESPN reported that Mata - sold by Jose Mourinho at Chelsea in 2014 - is keen to quit the Red Devils, with the Portuguese manager subbing him on and off again in Sunday's Community Shield win over Leicester City at Wembley.
Big things are expected from Everton this season after replacing Roberto Martinez with Ronald Koeman, and Carragher feels a top-four finish should be the aim - and believes that Mata could help them reach that level.
Asked by Squawka if Mata is among the players Everton should be targeting, Carragher said: "Yeah I think so. I think they should be looking at players who can take them close to the top four. That's got to be the aim of Everton."
Everton already boast an excellent squad and John Stones was speedily replaced by defender Ashley Williams earlier this week.
If they can keep star striker Romelu Lukaku and sign someone like Mata then Koeman might succeed where Martinez failed in getting the very best out of a fine collection of players.