Umar, 21, scored twice in six Serie A appearances for Roma during the 2015-16 season, but has spent time out on loan with Bologna, Torino and NAC Breda over the last couple of years.
Last term, the striker netted five times in 12 league matches for Breda, and Gerrard confirmed last month that he was interested in bringing the Nigeria Under-23 international to Scotland.
The former Liverpool captain has insisted that Umar remains a Roma player, but has said to "watch this space" regarding a potential deal.
"At the moment he is still a Roma player but it has been well documented that I am a fan, but it's just a case of watch this space," Gerrard told reporters.
"It is difficult to say whether it will be done before the first leg [of Europa League qualifying on Thursday], but we will be doing more business."
Rangers started their pre-season with a 6-0 win over Bury on Friday night.