The highly-rated 24-year-old has earned rave reviews for his performances in Ligue 1 over the past 12 months and Arsene Wenger is thought to have identified him as a transfer target for this summer.
Reports suggest that the Gunners have already had two bids for Koscielny rejected by the French club but are determined to secure his services.
Strengthening the defence is a priority for Wenger as it is still unclear whether out-of-contract duo William Gallas and Sol Campbell will be staying at Emirates Stadium.
Arsenal's initial offer for Koscielny was believed to be in the region of £4million, while they were then prepared to do a deal that would also involve youngster Francis Coquelin moving on loan in the opposite direction.
The Gunners have now lodged a bid of £8.2million, according to reports, although Lorient are determined to keep hold of their key men.
"We do not need to sell," chairman Loic Fery said in the Daily Mirror.
"We are fortunate to have a solid financial structure."