And it that’s because the Cherries do not want to sell despite signing Dominic Solanke from Liverpool.
The youngster is not expected to play for Bournemouth until February at the earliest because of a hamstring injury.
And Eddie Howe is desperate to keep hold of Wilson this month as a result.
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The England international has netted nine times in the Premier League this season.
That has alerted Chelsea to his talents with Maurizio Sarri looking to sign a striker this month.
Alvaro Morata and Olivier Giroud have both struggled as the main forward for the Blues this season.
And that has led to Eden Hazard being given the role of leading the line in recent matches at Stamford Bridge.
But signing Wilson could prove a tough task this month.
Bournemouth have no reason to sell despite signing Solanke from Liverpool for £19million.
The Mirror claim the loan exit of Jermain Defoe to Rangers has also helped to free up money for the Cherries.
Selling Wilson would mean Howe would be overly reliant on Solanke who will need time to get back to full fitness following his hamstring problem.
Chelsea assistant Gianfranco Zola confirmed the club were monitoring Wilson last month.
He explained: “Callum is doing well and is of interest not only for us but for many.”
The Blues top target is said to be Gonzalo Higuain.
Sarri previously worked with the Argentine during his time as Napoli manager.
Chelsea return to action tomorrow night when they take on Tottenham in the first leg of their Carabao Cup semi-final.