Having previously shown an interest in the Argentina global during the summer transfer window, Maurizio Sarri made it clear to the Chelsea hierarchy he was keen to reunite with a player who thrived under him at Napoli.
He also made headlines in November when he was sent off against his parent club, with his reaction to the decision earning him a two-match Serie A suspension.
Shearer feels a top-four finish on the Premier League table would represent a good opening campaign for Sarri.
Chelsea started struggling striker Alvaro Morata up front in hopes of the Spain global rediscovering his goal-scoring form but debutant Saints' goalkeeper Angus Gunn was the star in an otherwise lacklustre Premier League encounter.
Chelsea confirmed on Wednesday that they had reached an agreement with Borussia Dortmund over a €64million transfer for the United States global.
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"I think he [Sarri] will be quite content at where they are", Shearer said on BBC Radio Five Live.
The Premier League club have not been able to rely on their strikers for goals this season, as Olivier Giroud and Alvaro Morata have managed just six between them.
"We have to try to solve the problem of the last 15 or 20 metres because in the last matches we were in control of the match but for us it's not easy to score the first goal".
Shearer added: "Is Sarri-ball when they ask a midfielder to get on the ball and pass it around".
Chelsea will be gunning for victory against the Saints who have enjoyed an improvement under new boss Ralph Hasenhuttl.