A source told the Evening Standard that Rupert Murdoch has ordered News International to pay for the medical expenses for the reporters.
The alleged incidents occur amid investigations into alleged bribery of public officials by journalists at The Sun, which has led to the arrests of 11 current and former staff at the paper.
Three sources also confirmed to Reuters the alleged suicide attempt by two senior reporters.
A News International employee suggested that staff at The Sun felt under attack from the Management and Standards Committee set up by News International's parent News Corp, which has been working with the authorities.
"People think that they've been thrown under a bus," they said. "They're beyond angry - there's an utter sense of betrayal, not just with the organisation but with a general lynch-mob hysteria."
A senior News International source added to the Evening Standard: "These former journalists are turning their own people over to police for 'crimes' that newspapers have indulged in for centuries.
"I doubt whether Will Lewis and Greenberg will be able to show their face around News International. They have both s**t all over their colleagues."
Other sources claimed that journalists at the paper's Wapping headquarters are "terribly stressed and many are on the edge".
News International is reported to have increased the amount of psychiatric help on offer to employees to help them cope with both the investigations and the extra workload of producing the new Sunday edition of The Sun.