Over its long history of usage, the meaning of 息 has evolved.
Yes, 息 has the connotation of message.
(5) 消息 [message]
(6) 又如:信息(音信;消息);息耗(消息,信息)
Its original meaning is to breathe;pant.
(会意兼形声。从心,从自,自亦声。自,鼻子。古人以为气是从心里通过鼻子呼吸的。本义:喘气;呼吸)
And then the meaning was extended,
人之氣急曰喘。舒曰息。引伸爲休息之偁。又引伸爲生長之偁。引伸之義行而鼻息之義廢矣。
[ Breathing slowly was called 息, and it extended again to mean rest, and extended again to mean grow. ]
And then it became to be used with its antonym 消 (get rid of;eliminate) as 消息 from pre-Qin period (先秦), means 增减;盛衰 (growth and decline), and then extended to mean 变化 (change).
Then 消息 began to be used to mean 情况 (circumstances;situation;condition).
到了魏晋时期,“消息”的涵义则多为“情况”了.
任何事物都会有从生长到死灭、从兴盛到衰败的发展变化过程,这种变化过程是一种“情况”.所以“消息”从“消长(生死盛衰)”的涵义演变为“情况”的涵义。
[ By the Northern and Southern Dynasties, 消息's primary meaning was situation. The process of evolution is a kind of situation, so 消息's meaning was extended from changing to situation. ]
到了南北朝后期,“消息”便又发展出“音信”、“音讯”的涵义,而且从此就成为“消息”最主要的意思.
[ By the later stages of the Northern and Southern Dynasties, 消息's meaning was further extended to mean 音信 (mail;message;news) and 音讯. And that became its primary meaning.]
Reference:
释息
“消息”的词义演变历程探析
从消息到信息──词义的变迁与汉语教学隅例
息could meanmessagealone, but (1) zdic.net gives it an item of the meaning消息 [message], (2) besides消息, there're信息/息耗meaningmessagetoo, so I think "息has meaning ofmessage" should be fine. (It's not equal to "its meaning ismessage" for me. Maybe should say has potential meaning ofmessage? Sorry I'm not sure about the English expression here.) – Feb 15 '16 at 14:48