Arsenal boss Unai Emery is keen to strengthen his side in the transfer window this summer but is working on a restricted budget.
Inter, meanwhile, are eager to move Icardi on with the Argentina international not in Antonio Conte’s plans for next season.
The Serie A giants are understood to be chasing Manchester United hitman Romelu Lukaku who, after just two years at Old Trafford, is keen to make the move.
And Italian website Calcio Mercato claim that Arsenal have enquired about Icardi’s availability.
However, Inter refused to consider a cash transfer.
But they did demand a direct swap deal involving Pierre-Emerick Aubameyang, who top-scored for the north London giants last season.
The Arsenal striker has been linked with a move to Manchester United despite Ole Gunnar Solskjaer’s determination to sign younger players.
Yet a transfer will not be happening.
The report claims Icardi snubbed Arsenal’s approach anyway with the forward keen to play for a team in the Champions League.
United have also turned down the possibility of taking the Argentina international as part of any Lukaku swap deal.
And it remains to be seen where Icardi will end up with Inter so determined to cut him loose.
Meanwhile, former Inter sporting director Walter Sabatini recently lauded Icardi.
But he did so in rather bizarre style, appearing to aim a dig at the player’s wife Wanda Nara.
“If Icardi was my player, I’d find a boyfriend for Wanda,” he said.
“So that she stepped away from Mauro, who’s a wonderful lad and a loving father.”
Arsenal are hopeful of securing four signings this summer.
A loan deal for Dani Ceballos appears to be edging closer with Real Madrid happy to let the Spain international go for a season.
Celtic’s Kieran Tierney and Crystal Palace’s Wilfried Zaha are also on Emery’s wishlist.
And so too is a new centre-back amid the struggles of Shkodran Mustafi last term.