Olivier Giroud was top of Roma's list of transfer targets had Chelsea met the asking price for Edin Dzeko, according to the Serie A club's sporting director Monchi.
Although the Premier League champions signed defender Emerson Palmieri from the Giallorossi, Roma rejected offers for striker Dzeko.
Giroud eventually moved from Arsenal to Stamford Bridge as part of a deadline day transfer triangle that saw Michy Batshuayi head to Borussia Dortmund on loan as a replacement for Pierre-Emerick Aubameyang, who became the Gunners' record signing.
And Monchi confirmed Roma had Giroud in their sights if Chelsea had met the asking price for former Manchester City striker Dzeko.
"We would have signed another important player, perhaps Giroud, because otherwise the fans would have been really unhappy," Monchi told Sky Italia.
"The English club [Chelsea] never met our financial demands so the deal was never closed.
"No club are happy to sell their best players, but if a good offer arrives, it's important to evaluate it."
Giroud, yet to score for Chelsea, has described joining Antonio Conte's side as the "obvious" choice, with Dortmund and Sevilla having also been keen on the France international.