The Old Trafford boss admits he is loathe to leave the Mexico international out when he is in such fine form, but says he must replace him for Robin van Persie in some games
The 71-year-old manager signed Robin van Persie from Arsenal for £24 million in the summer, and the Holland striker has dazzled Old Trafford with 22 goals in just 28 appearances in all competitions.
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"It's a terrible dilemma when I've got that lad [Chicharito] there," he told reporters.
"Sometimes I leave him out to bring in Robin van Persie but, as I explain to him, we regard him so highly.
"He's a fantastic professional, unbelievable attitude to the game, never stops running or working and every training session’s the same.
"So I'm really pleased for him and it's also good to see Wayne [Rooney] back scoring."
Chicharito's latest double eased his side to a 4-1 win over Fulham in the FA Cup fourth round on Saturday, while they lead the Premier League table by five points and contest Real Madrid in the last 16 of the Champions League.
And while recent results leave fans quietly wishing for another attempt at a historic 'treble' season, Sir Alex insists his side have to be wary of the threat posed by Southampton, who United host on Wednesday evening in the league.
"[Southampton] played really well against Everton who are at the top of their game and playing really well, so we're not taking anything for granted," he added.
"They should have won as they were superb and could have been five-up in the first half.
"Tim Howard had a fantastic game, they hit the woodwork and Rickie Lambert missed a couple of chances."