Lingard is currently a free agent after leaving South Korea's FC Seoul at the end of the K-League season.
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The midfielder, now 32, is in talks with Scottish Premiership, Premier League and Serie A clubs as he weighs up his next move.
The Daily Mail says Lingard is favouring a move to Italy, where he is fielding interest from several Serie A teams.
Last month, upon leaving FC Seoul, Lingard posted to social media: "My time in South Korea has been unbelievable – the football, the atmosphere and the passion around this club have been top class.
"The love, support and the appreciation you have shown towards me for these last two years has been truly amazing. I'll always be grateful for the opportunity to play for such a massive club."