Koscielny has been in superb form so far this season, and has formed an impressive partnership at the back with Per Mertesacker.
Although the 28-year-old still has three years to run on his contract with Arsenal, his representatives have already opened talks about an extension.
Such is his reputation as one of the Gunners' best players that, according to the Mail, he will be offered £90,000-per-week to sign on the dotted line, which would put him on par with the second-highest earners at the club, just behind record buy Mesut Ozil.
A deal of that size may be required in order to persuade the Arsenal man to ignore the interest of Chelsea and Manchester United.
The Mail claim that various European clubs including Bayern Munich and Real Madrid are keeping tabs on Koscielny's situation, and are ready to make their move.
Chelsea have options at the back with David Luiz, John Terry, Gary Cahill and Branislav Ivanovic - although reports suggest Luiz could be on his way out of the club.
Manchester United are also blessed with plenty of centre-backs, although there could be an exodus in the summer with Rio Ferdinand likely to leave alongside Nemanja Vidic, who is joining Inter Milan.
Arsenal have been busy tying down a host of players to new contracts in recent months, with Santi Cazorla, Aaron Ramsey, Tomas Rosicky and Per Mertesacker all committing their future to the club. Bacary Sagna looks likely to be the one that gets away; his deal is up in the summer with no agreement in place.
Manchester United take on Everton tomorrow, while Chelsea go up against Sunderland and Arsenal face Hull at the KC Stadium.