Mourinho appeared to send a message to the club by posting an image of himself and his staff embracing an invisible man on Instagram at the end of Roma's pre-season training camp in Portugal a week ago.
"There was no provocation, that wasn't the intention," the 60-year-old told Italian newspaper Corriere dello Sport. "Everything is not okay, but I get angry for an hour and then I'm back to being positive about things.
"Regarding the imaginary striker, I can tell you that even if (Kylian) Mbappe arrives next week, it would still be late."
English striker Abraham suffered an anterior cruciate ligament (ACL) injury on the final day of last season and is not expected to play again this year.
Roma, who finished sixth in Serie A, were linked with Spain striker Alvaro Morata (30) and Atalanta forward Gianluca Scamacca (24) but neither signing has materialized, with Mourinho's team set to kick off the new season at home to Salernitana on Aug. 20.
"After Tammy's injury we are in a situation that no coach in the world would like to be in. It is impossible for me to say that I am happy. But to say that I am in open war with the club is very wrong," Mourinho said.
"Tammy was injured on June 5, we are talking about 63, 64 days (ago). For me there is a name, there is one, because I am usually very objective and pragmatic, but it is not possible to get him. This is what I was told."
Roma were one of eight clubs that reached settlements with UEFA last season after failing to comply with break-even requirements the previous campaign.
The Italian club paid a fine of five million euros ($5.50 million) and are liable for an additional 30 million euros if they do not comply with UEFA's sustainability regulations by the 2026-27 season.
Roma have had a quiet transfer window as a result, signing free agents Evan N'Dicka (23) and Houssem Aouar (25) and bringing in Rasmus Kristensen (26) on loan from Leeds United.
Their most significant piece of business has been retaining the services of Argentina forward Paulo Dybala.
"When Aug. 1 arrived and (Dybala's) release clause could no longer be activated, I slept easier. He is of the highest levelmand we can't do without him," Mourinho said.
