The France international is thought to be facing an uncertain future at Ligue 1 champions Paris Saint-Germain due to their financial restrictions.
Mbappe scored 13 goals and made eight assists in 27 games in Ligue 1 following his loan move to Parc des Princes from AS Monaco last summer.
The teenager netted four times and made three assists in eight outings in the Champions League to underline his rising status.
Champions League winners Real Madrid have also been linked with a swoop to sign Mbappe over the past 12 months.
Sky Sports News reporter Johnson is adamant that Manchester United won’t be signing the France striker in the current transfer window.
Asked about Mbappe moving to Old Trafford, Johnson told the Transfer Talk podcast: “Absolutely no chance.”
Manchester United finished in second place in the Premier League table last season to finish ahead of Spurs and Liverpool FC.
However, the Red Devils ended up 19 points adrift of English champions Manchester City.
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