Ulster head coach Dan McFarland says he "hasn't really spoken" to John Cooney about the scrum-half's potential switch from Ireland to Scotland.
New World Rugby rules mean Cooney, who won the last of his 11 Ireland caps in February 2020, can play for Scotland towards the end of February.
Scotland coach Gregor Townsend says Cooney reached out to him about a move.
But when asked if he had spoken to anyone regarding Cooney becoming a non-Irish player, McFarland replied: "No".
Irish provinces are allowed three 'NIQ' [Non-Irish Qualified] players in their squad to promote Irish players coming through from the provinces' respective academies.
South African World Cup winner Duanae Vermeulen, prop Jeff Toomaga-Allen and second row Sam Carter are currently Ulster's three NIQ players.
Scotland prop Rory Sutherland joined on a short-term deal after Worcester Warriors were placed in administration in October. All four players are out of contract in 2023.
Springboks prop Steven Kitshoff will join Ulster following the Rugby World Cup, while second row Dave Ewers will move to the province from Exeter Chiefs.
Previously this would not have been an issue for Dublin-born Cooney as he came through Leinster's youth system before joining Connacht. The 32-year-old moved to Ulster in 2017 to replace the outgoing Ruan Pienaar.
It remains to be seen as to exactly how any potential switch to Scotland will impact Cooney's position as a non-NIQ player.
Munster fly-half Ben Healy, who played for Irish age-group teams, was named in Scotland's Six Nations squad and will join Edinburgh on a two-year deal in the summer, while hooker Bradley Roberts left Ulster for the Dragons in 2022 after he was named in Wales' squad.
However, both their circumstances are different to Cooney's as they did not play for Ireland's senior team before making their respective international switches.