The Gunners are keen to secure competition for Olivier Giroud, with the Stamford Bridge forward now top of their shortlist.
The report claims an €18m offer could be on the cards in January, although that is the maximum figure Arsenal boss Arsene Wenger would be willing to spend on the Senegal international.
Arsenal's shortage of quality alternatives to Giroud was highlighted last week when Nicklas Bendtner deputised for the Frenchman in the Capital One Cup defeat to Chelsea.
Injury to Giroud would seriously dent Arsenal's title hopes, with the club currently top of the Premier League standings by five points.
Ba is well down the pecking order at Stamford Bridge, with Jose Mourinho favouring Samuel Eto'o or Fernando Torres depending on the competition. Ba has made just two Premier League appearances this season and is yet to find the scoresheet.
And recent reports have even suggested the Chelsea boss is not happy with these options and is plotting a January swoop of his own for another new striker.
That would free up Ba to leave Stamford Bridge, with Arsenal thought to be monitoring developments.