According to Adrian Kajumba of the Daily Mirror, the Blues are ready to step up their interest in the forward, who has been in impressive form so far this season for the Cherries.
When asked about the rumours on Friday, Howe made it clear the club wouldn't be looking to cash in and emphasised that he's seeking to build something on the south coast, per Ned Payne of the Daily Echo.
"Of course not," he said when asked if the club would welcome any interest. "From my position, sitting here as the manager, I'm looking to build a team. I still feel we are a relatively new team with this group of players and the signings we made in the summer."
Links to elite clubs in the Premier League may not come as a big surprise in regards to Wilson, as he appears to have taken a step up this season.
Already he's been on the scoresheet seven times in all competitions for Bournemouth in 2018-19, including grabbing the opening goal last weekend in the 2-1 loss against Manchester United.
Wilson's form has also earned him a call-up to the England team for the first time in his career:
Per Squawka Football, there haven't been many players eligible for the Three Lions who have been able to match Wilson's productivity at this level:
It's not just the goals that make the Bournemouth man such a handy footballer to have up top, though.
This season there have been clear developments in his game. Wilson has always been mobile and physical, although this term he appears to be using his frame better than ever to hold off opposition defenders and bring others into the game.
Alongside the likes of Ryan Fraser, David Brooks and Josh King, he's been part of a devastating Bournemouth attack. With Wilson offering a pragmatic and prolific focal point, managers from clubs with bigger reputations will no doubt be looking on.
Additionally, Wilson has shown a tremendous attitude to battle back from a number of injury issues to get back to the top level:
2012: Playing in the Conference with Tamworth ⚽️ 2014: Signed for Bournemouth for £3m 🍒 2015: Promotion to the PL 👏 2015: Ruptured ACL in right knee 🤕 2017: Ruptured ACL in left knee 🤕 2018: Receives first ENG call up 🏴 What a journey for Callum Wilson! #AFCB https://t.co/k0yDjPkdwU
At the moment, Chelsea are alternating between Olivier Giroud and Alvaro Morata at the top end of the pitch.
Giroud offers a physical presence and is an excellent link man for Eden Hazard, while Morata is more mobile and at the moment more prolific. What manager Maurizio Sarri would want is a forward who can amalgamate those traits together.
Wilson is potentially that man, and you sense there will be a lot of eyes on his performances on the international stage as he seeks to take another step up in his career.
However, Howe's reluctance to entertain any offers for such a key man midseason will make this deal a tough one for any club to do, including Chelsea.