The Blues are believed to be on the lookout for further reinforcements this month despite having already secured the signing of Ross Barkley from Everton at the turn of the year.
Former Manchester City striker Dzeko, 31, has been touted as a possible target for the Blues in recent days as Antonio Conte looks to bolster his front-line.
Chelsea are also believed to be on the lookout for a new left-back, with Brazilian Emerson linked with a move to Stamford Bridge in the last few days as well.
Now, Sky Sports News reporter Solhekol has claimed that Chelsea are ready to pay around €50m in total for the signatures of both players – but Roma want a fee closer to €65m.
Solhekol wrote on Twitter: “Sky Italy – Chelsea want Edin Dzeko from Roma. Willing to pay €50m for Dzeko and left back Emerson Palmieri. Would also let Roma have Batshuayi on loan. Roma want €15m more.”
Chelsea are currently preparing for the second leg of their League Cup semi-final clash against Arsenal at The Emirates on Wednesday night.
The two London sides played out a goalless draw when they last met in the first leg at Stamford Bridge earlier in the month.
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