Indeed, Murphy says Tierney will never be as good as Scotland's current national team captain Robertson.
Asked if Tierney can reach Robertson's heights, Murphy told the Glasgow Evening Times: "No. Robertson just has an unbelievable, consistent performance level and mentality. The fitness he has got and the quality in the final third, I say no because the level is so high.
"He has set the bar as a left-back remarkably high. "He is in the top three in the Premier League for assists and what both fullbacks are doing at Liverpool is phenomenal.
"But Arsenal have got a really good signing there in Tierney and he is only going to improve."