Former Hearts striker Kevin Kyle is training with Rangers having done so with St Johnstone earlier this week.
The relaunched Ibrox club are still awaiting Scottish FA membership.
They want to take over the old Rangers' licence to play competitive matches but have yet to finalise an agreement with all interested parties, including the SFA, Scottish Premier League and Scottish Football League.
St Johnstone manager Steve Lomas said earlier this week he was still waiting to know what his budget would be for the new season and still hoped to add "four or five" players to his squad.
"A fit Kevin Kyle would certainly be an asset to any club," the Saints boss told BBC Scotland.
Kyle, 31, had also alluded to possible interest from Hearts' Edinburgh rivals Hibernian earlier this summer.
Capped 10 times for Scotland, he spent much of his career in English football before joining Kilmarnock in 2009 and Hearts the following year.
His last competitive appearance came in a January 2011 Scottish Cup tie in-which Hearts were beaten by Saints.
He left the Tynecastle club 14 months later by agreeing an early termination of his contract and has spent the summer working on his fitness.