Nole began his Roland Garros 2016 campaign on Tuesday, defeating world no.95 Yen-Hsun Lu 6-4, 6-1, 6-1.
The 2010 champions will host 2015 title holders Great Britain in the Davis Cup by BNP Paribas World Group quarter-finals on July 15-17.
Andrey Golubev and Aleksandr Nedovyesov defeated Djokovic and Zimonjic 6-3, 7-6 (3), 7-5 to hand the visitors a 2-1 lead.
Nole headlines Serbia’s team nominations and will be joined in the line-up by Viktor Troicki, Filip Krajinovic and Nenad Zimonjic.
Novak cruised into the second round of the Dubai Duty Free Tennis Championships with a 6-1, 6-2 win over world no.41 Tommy Robredo.
The top seed needed just 70 minutes to routinely beat Joao Souza 6-1, 6-1, 6-1 in their first-round match at the US Open 2015 on Monday.
Defending champion beat German Philipp Kohlschreiber in two hours and two minutes on Monday to reach the second round.
Novak began his quest for a first Roland Garros crown with a 6-2, 7-5, 6-2 victory over 87th-ranked Jarkko Nieminen on Tuesday.
Novak and Viktor both won on the opening day at Kraljevo Sports Centre to give Serbia a 2-0 lead over Croatia going into Saturday’s doubles.
Kraljevo, Day 1: 13.00 CET Novak Djokovic (SRB) vs Mate Delic (CRO), followed by Viktor Troicki (SRB) vs Borna Coric (CRO).