Former Manchester United star Evans is available for just £3m due to a relegation release clause in his contract.
Arsenal have a long-term interest in the Northern Ireland international, having failed with an offer worth £10m plus right-back Mathieu Debuchy in January.
According to TransferMarketWeb, Gunners chiefs are trying their luck again, this time tabling a cash bid for his signature.
An exact fee is not mentioned but it would likely meet Evans bargain buyout clause.
Despite a disappointing campaign for West Brom, Evans is hot property ahead of the summer transfer window.
Premier League champions Manchester City also fancy swooping for the Northern Ireland international.