Both clubs have had bids for the Republic of Ireland international accepted by The Lions and are set to hold talks with the midfielder but Pompey's offer of first team football may swing the balance in their favour.
Rovers have been long-standing admirers of the 22-year-old and have had previous offers of £2 million rejected by the First Division club. But despite playing for the Republic in last summer's World Cup finals, Souness does not consider the 22-year-old to be an automatic first choice, which has surprised many in the game.
"We've been given permission to speak to the player but we are a long way from signing him," said Souness.
"Steven is one for the future but he would give me valuable cover."
This could prove to be a stumbling block in negotiations for a player who has made over 150 appearances for the Lions since his debut in 1998.