International duty meant just nine first-team players were present at Melwood as the former Borussia Dortmund boss began work proper on Monday afternoon after his appointment last Thursday.
Coutinho, who a week ago pulled out of Brazil's squad for World Cup qualifiers against Chile and Venezuela with a minor groin injury, was involved and early indications are the 23-year-old will be available for Klopp's first match in charge at Tottenham on Saturday lunchtime.
Other first-teamers present for the session which lasted just over an hour were James Milner, Daniel Sturridge, Mamadou Sakho, Alberto Moreno, Lucas Leiva, Kolo Toure, Dejan Lovren and Joao Carlos Teixeira.
With the first six of those plus Coutinho all realistically in with a good chance of starting at White Hart Lane, Klopp at least had a decent base on which to begin his planning for the game.
The remainder of Liverpool's internationals are expected to return to Melwood by the middle of the week, giving the German three days to work with his full squad - minus the likes of captain Jordan Henderson, striker Christian Benteke and forward Roberto Firmino who are all still out injured.
Klopp spoke to those assembled players present on Monday in a huddle for five minutes before training commenced under him, Peter Krawietz, Klopp's analyst and scout at Borussia Dortmund, and existing first-team coach Pep Lijnders - both of whom were at the club's academy with the German on Saturday to watch Liverpool's Under-18s beat Stoke.
Zeljko Buvac, Klopp's long-time assistant, is yet to arrive on Merseyside.