Arsenal attempted to sell Alexandre Lacazette and replace him with Tammy Abraham in the summer, according to reports.
Chelsea sold Abraham to Roma last month for an initial fee of £34m, and the striker has made a fine start to life in Serie A.
The England international has scored one goal and provided two assists in three appearances in Italy's top flight.
"They were trying to convince the player and to take his time before joining Roma because they were looking to sell maybe Lacazette or maybe Eddie Nketiah to have a free slot for a new striker with Tammy Abraham," Romano said.
"They were really interested, in talks with the agent, but they were prepared to make a proposal. But they were needing to sell a striker before signing Tammy Abraham.
"They were really, really pushing and pushing, they were trying in every possible way.
"So, Arsenal were really convinced that they had a chance to sign Tammy Abraham but in football it is not easy to change the mind of the players."
Arteta's side picked up their first win of the season by beating Norwich 1-0 on Saturday.
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