The England captain could only manage scores of 19 and 5 as his side were thrashed by Pakistan in the first Test in Dubai last week and has failed to record a Test century since the back end of 2010.
The pair are poised to open the batting together for the 100th time in Test cricket next week and Cook is confident that Strauss can rise to the occasion and recapture his best form.
"He's got a great record and has proved that over a number of years," he said.
"It's always nice for our stability with Strauss at the top of order. We have had some great moments. We are pretty similar in character and we do enjoy batting together and hopefully on the 100th time we will do something special."
The duo average 42.90 for England's first wicket and have both recorded 19 Test centuries.