The France international is set for a run in Garry Monk's starting XI, with star frontman Wilfried Bony having left to join up with Ivory Coast at the Africa Cup of Nations.
Gomis has just one Premier League goal to his name since arriving in south Wales from Lyon for the 2014-15 season, but bagged a brace in Saturday's 6-2 FA Cup victory at Tranmere Rovers.
And Fabianski believes Bony's absence presents Gomis with the chance to prove his worth to Swansea.
"Bafe came on at Liverpool [last Monday's 4-1 defeat] and looked dangerous, while he was very positive against QPR [a 1-1 draw on New Year's Day]," he told the club's official website. "He has waited a long time for a run in the team, but he will get it now and I'm sure he will deliver for us.
"We are also without Ki [Sung-Yueng], but we also have players in that position to come in and do a very good job.
"Wilfried and Ki have played very well for us this season, but their absence means there are opportunities for the likes of Bafe to possibly have a run in the team and show why they deserve to stay in the starting XI."
Swansea host West Ham in the Premier League on Saturday.
