Portuguese daily O Jogo claim that around 50 hooded men stormed the Lisbon club's base and went at staff with batons and makeshift weapons.
Images have emerged of what appears to be Dutch international Dost with two nasty cuts on his forehead.
TVI24 report that a physio was stabbed during the ambush.
Boss Jorge Jesus, skipper William Carvalho and vice-captain Rui Patricio were said to have been targeted, along with Marcos Acuna and Rodrigo Battaglia.
All the players are now said to be looking to quit their contracts.
There is also a a suggestion that players could pull out of this Sunday's Portuguese Cup final against Aves.
Sporting missed out on a Champions League spot on Sunday after a 2-1 defeat to Maritimo.
And fans appear to have reacted furiously, with their club posting a statement on Facebook.
It read: "Sporting vehemently condemn the events at the Sporting Academy today.
LIS-BURN Sporting Lisbon in chaos: President ‘suspends’ manager Jorge Jesus — and players ‘boycott cup final’ as show of solidarity
"We cannot in any way agree with acts of vandalism and aggression to athletes, coaches and staff, nor with attitudes that constitute crime that in no way honour and ennoble Sporting.
"Sporting is not this, Sporting cannot be this.
"We will make every effort to establish full responsibility for what has happened and we will not fail to demand punishment for those who acted in this absolutely pitiful way."
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