The Blues offered £46m (€60m) for Mkhitaryan last summer but were knocked back by the German giants, according to the Daily Star.
They are set to go back in for the Armenia international and TransferMarketWeb claim a ‘majestic cash offer’ is ready to be launched.
Mkhitaryan has enjoyed a phenomenal season for Dortmund, scoring 23 goals and creating a further 32 in 51 appearances.
However, Chelsea face competition from Arsenal for the 27-year-old.
Arsene Wenger reportedly views Mkhitaryan as a potential replacement for Alexis Sanchez with doubts surfacing over the Chilean’s future.
Arsenal are willing to meet his £8m-per-season contract demands after tracking his progress.
Italian champions Juventus are also keen on Mkhitaryan, who is about to enter the final 12 months of his contract.