Chairman Dave Pottinger did not name the club that made the offer but insisted it was nowhere near their valuation for the Wales Under-21 international.
Pottinger also insisted the 21-year-old, who joined Town from Swansea in August 2012, remains a vital part of manager John Gregory's plans for the future.
He wrote on Twitter: "Today the Board turned down a bid of £400,000 for Joe Walsh. The offer is way under his valuation. Joe Walsh is a big part of our plans."
Walsh has made 23 appearances for Crawley this season and scored five goals.