Benitez is known to be concerned that his contract has been allowed to
run down so close to its end."
"... he wanted to give his manger an extension but has now gone omiously quiet on the subject"
Right, these two sentences are explanations, could be rephrasing, complementary info.
run down means let it go, let time pass, as a river runs down.
omiously is the way a teacher approaches a student when the student behaved badly, as in an assertive way.
It is a common spelling mistake, should read ominously, as in:
3 dictionary results for: ominously
Dictionary.com Unabridged (v 1.1) - Cite This Source - Share This om·i·nous 
/ˈɒmənəs/ Pronunciation Key - Show Spelled Pronunciation[om-uh-nuhs] Pronunciation Key - Show IPA Pronunciation –adjective | 1. | portending evil or harm; foreboding; threatening; inauspicious: an ominous bank of dark clouds. |
| 2. | having the significance of an omen. |
[Origin:
1580–90; < L
ōminōsus portentous, equiv. to
ōmin- (s. of
ōmen)
omen +
-ōsus -ous]
om·i·nous·ly, adverb
om·i·nous·ness, noun
—Synonyms Ominous, portentous, threatening, menacing, fateful are adjectives describing that which forebodes a serious, significant, and often harmful outcome. Ominous, derived from omen “a predictor of outcomes,” usually suggests evil or damaging eventualities: ominous storm clouds; an ominous silence. Portentous, although it may suggest evil results, often stresses a momentous or very important outcome: a portentous moment in history; a portentous escalation of hostilities. Threatening may suggest calamity or great harm but sometimes mere unpleasantness: a threatening rumble from the volcano; A threatening look from his brother caused him to quickly change the subject. Menacing always suggests serious damage as an outcome: a disease menacing the entire population; He advanced with a menacing swagger. Fateful most often stresses the great or decisive importance of what it describes: a fateful encounter between two future leaders; a fateful day that changed our world.