The former Sweden international re-signed with Manchester United last month after the Red Devils released the experienced centre-forward earlier this month.
The 35-year-old moved to Manchester United in a free transfer from Ligue 1 giants Paris Saint-Germain last summer.
Ibrahimovic scored 28 times in all competitions last season to help Manchester United to win the EFL Cup and the Europa League.
Manchester United spent a £75m transfer fee on Belgium international Romelu Lukaku in the summer transfer window as the Red Devils beat title rivals Chelsea to the signing of the Everton striker.
Lukaku has already scored four goals in four Premier League games to help Manchester United hoist themselves to the top of the Premier League table.
However, former Manchester United defender Parker believes Ibrahimovic could have a big role to play in the Champions League for the Red Devils this season.
“That’s why I think Zlatan (Ibrahimovic) could play a bigger role in Europe than he does in the Premier League this season,” Parker told Eurosport.
“If he comes back in November, December or January – whenever it may be – then when United start the knockouts in February, providing they make it, it will be Ibrahimovic who leads the line and Lukaku will be on the bench, without a shadow of a doubt.”
Manchester United are looking to win the Champions League for the first time since 2008.
Ibrahimovic has won countless Serie A titles, La Liga crowns, Ligue 1 titles but the Swedish striker has never won the Champions League or the Premier League.
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