The Blues spent a club-record £97.5m to re-sign Romelu Lukaku over the summer, and the Belgium international has scored four times in 11 appearances for the capital outfit since his return.
Lukaku is currently on the sidelines with an ankle problem, though, and according to transfer expert Ian McGarry, Tuchel is wary of relying too heavily on the centre-forward for goals.
As a result, the Chelsea manager has allegedly instructed the club's board to move for a new attacker when the winter transfer window opens for business.
"It is our information that he [Tuchel] has requested from the club that they recruit a striker in the January window," said McGarry on The Transfer Window Podcast.
"From what I'm told, there is no definite shortlist that's been formulated as yet, but you can see the point that they've been heavily reliant on Lukaku in such a short space of time since he arrived back at the club for his second spell.
"This has been significantly influenced now as well by the fact Romelu Lukaku will miss at least two games but maybe up to a month in the coming weeks, as well as Timo Werner being out as well."