Gazzetta Dello Sport says the duo are set to be handed new contracts in an effort to keep the Red Devils at bay.
Inter captain Icardi is one of the deadliest strikers in Europe, having scoring 100 goals in 160 Serie A matches.
While Skriniar has established himself as a top young centre-back following a barnstorming debut season at the San Siro.
It's claimed that United are interested in bringing both players to Old Trafford following a shaky start to the Premier League campaign.
But Inter have no intention of selling either player, and will now look to tie them both down to new deals.