Porto beat the Italian side 3-1 (4-3 agg) at home last to send them out of the Champions League.
Some reports had claimed Monchi could join Arsenal as their new technical director before the end of the month if they lost to Roma.
The 50-year-old Spaniard is top of the Gunners' hit list to oversee operations at the Emirates.
And Marca, quoting Italian media, have suggested a move is even nearer to completion after Monchi let rip at raging Roma supporters.
Ultras reportedly shouted "you have to go" and "you're wrecking the team" at Monchi.
But he is said to have hit back: "You're fine. In six months I'll come to look for you one by one."
Edin Dzeko – who channelled his inner Pepe by falling to the floor pathetically after a coming together with Pepe – was also verbally attacked by fans.
Steven Nzonzi and Patrik Schick were also confronted, according to reports.
Porto advanced after Alex Telles netted from the spot in the 116th minute.
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