Roberto Mancini’s side are currently sitting fifth in Serie A, two places outside qualification for next season’s competition.
Inter have not been in the Champions League since 2011, causing them to miss out on the vast amounts of money involved.
After sitting top at Christmas this season, it was hoped the club would return to Europe’s premier club competition.
But a drop in form has seen them slide down the table and now, according to Corriere dello Sport, Inter are ready to sell Icardi if they do not book a spot.
The striker’s departure would cause a significant boost to the club’s finances as he would command a fee of over £30m.
Arsenal and Chelsea have a long-term interest in the Argentina international, while Manchester United are on the hunt for attacking reinforcements this summer.