It is thought that Souness believes Thompson would make a good balance for Keith Gillespie on the right.
Several other clubs, including Everton and Manchester City, have also showed serious interest in the former Liverpool player. Rovers, however, having so far put up what is suspected to be the best offer of £3.5million, are looking like the favourites.
Initial offers from several clubs were refused by Coventry who wanted £4.5million for the 24-year-old. They are now thought to be planning to sell at a slightly reduced price. Their suspecting asking price is now £3.5million - perfect for Rovers...
Coventry chairman Mike McGinnity said last week: "We have had plenty of offers for Thommo but none have so far come anywhere near our valuation of the player.
"I'm sure we will sell the players we have earmarked but I will reiterate the fact that I have a responsibility to the club and I will not sell the family silver for nothing."