Robertson has not started the last two matches due to an injury sustained on international duty but looks set to return for Saturday's visit of Southampton.
In his absence Tsimikas, in his second season at Anfield after a Covid-impacted maiden campaign, has impressed to the point where he is putting pressure on Robertson's previously-undisputed spot as regular starter.
But Klopp has dismissed suggestions the Scot, who has been one of the club's most over-worked players in the last three years, is not in his best form and insists he retains his total trust.
"It is pushing but I don't see it as pushing in that sense," he said on the left-back competition.
"Robbo is Robbo and it is just a bit strange people constantly forget how good Robbo is just because in these moments Kostas is good as well.
"Thank God he is good or we would have a problem. Before we had no real solution and Milly (midfielder James Milner) had to play there and did really well but now we have a different solution, that's good.
"We have Kostas and Owen Beck coming up, a real prospect, so that's good for us but I don't doubt Robbo at all.
"Really happy about the development of Kostas, really happy, but Robbo is Robbo, an outstanding player.
"I don't know if he had drops in performance here and there but it doesn't change my mind because you can't trust people today and not trust them the next day.
"You have to show these kind of things as that's how you get the best long-term out of players.
"But I'm really happy Kostas shows how he showed up, an outstanding player.
"Robbo needed half-a year (to settle in), Kostas needed a year but now we see how good he is."