Antonio Conte's side finds itself bottom of the pool after the first four rounds of matches, but victory on Wednesday and defeat for Galatasaray would move it into second.
Antonio Conte's men failed to win any of their first four games in Europe's premier club competition and sit bottom of Group B with three points.
However, thanks mainly to the dominance of runaway pool leader Real Madrid - which has taken 10 points from its four games, scoring 14 goals in the process - Juve is still just one point behind Galatasaray and Copenhagen.
That means the Italian champions could end matchday five in control of their own destiny in terms of reaching the last 16, as a home victory over the Danes - coupled with a defeat for Galatasaray at Santiago Bernabeu - would put them second with just one game remaining.
Conte's side is sure to head into the crucial fixture high on confidence after it moved to the summit of Serie A by recording its fifth straight league win with a 2-0 success at Livorno on Sunday.
Fernando Llorente continued his rich run of form by opening the scoring with his third goal in as many games at club level before the Spaniard set up strike partner Carlos Tevez to end a run of three matches without scoring that sealed the points.
Juve has not won in its last three home Champions League games, but is unbeaten in 12 in all competitions on its own patch, a run stretching back to last season's quarterfinal defeat by Bayern Munich.
Copenhagen, meanwhile, head to Turin buoyed by its 1-0 victory over Galatasaray on matchday four.
Stale Solbakken's team has not lost in six games in all competitions and comprehensively overcame Viborg 4-1 in its last Superliga fixture on Sunday, with forward Igor Vetokele scoring twice to take his tally to seven for the season.
Juve needed a second half equalizer from Fabio Quagliarella to take a point from the reverse match at Parken in September, but the Danish champions have conceded seven goals in their away games at Real and Galatasaray this term.