The Hyderabad MP has sought police permission for the march, proposing three possible routes.
Owaisi tweeted on Wednesday that he made an application to the Hyderabad Police Commissioner, seeking permission for the march. He proposed three possible routes including one from Darussalam, the headquarters of AIMIM to Eidgah Bilali and another from historic Charminar to Dharna Chowk.
If the police accords permission to Majlis for January 4, it will clash with the 'Million March' planned by various Muslim organisations.
The Joint Action Committee (JAC), comprising various Muslim groups, on Tuesday urged the Police Commissioner to grant permission for 'Million March' on Necklace Road on January 4.
The JAC had originally planned the march on December 28 but the police denied permission for the same. It had then approached the High Court, challenging the police action.
JAC Convenor Mushtaq Malik said the High Court directed the police to consider a fresh request for permission for the march.
Following Owaisi's tweet on Wednesday, some netizens appealed to him to allow Million March as planned and defer his party's rally to January 5.
AIMIM has not yet organized a protest march though it, along with several other Muslim groups, held a massive public meeting at Darussalam on December 22 to oppose CAA and National Register of Citizens (NRC).
The MP had also led a delegation of Muslim leaders to meet Telangana Chief Minister K. Chandrashekhar Rao on December 25, urging him to not to conduct National Population Register (NPR) process in the state.
Meanwhile, Owaisi slammed state Congress chief Uttam Kumar Reddy for using what he called "intemperate" language against Hyderabad Police Commissioner Anjani Kumar.
The opposition party had Tuesday met Governor Tamilisai Soundararajan, demanding action against the Police Commissioner for his handed bhevaiour and denial of permission to 'Save India Save Constitution' rally in protest against CAA, NRC and NPR on December 28.
The Congress delegation led by Uttam Kumar Reddy complained to the Governor that the police was giving permission to AIMIM, which is an ally of ruling Telangana Rashtra Samithi (TRS).
"Even RSS was allowed to take out march in the city with lathi-wielding cadres," he said.
Responding to the Congress leader's remarks about AIMIM, Owaisi tweeted that he must understand that Darussalam is a large space of AIMIM itself and had once even hosted Indira Gandhi's public address.
The AIMIM chief also had a dig at Congress leader for rejecting his invitation to join a public meeting against CAA at Nizamabad.
"He was so enthusiastic about protesting against CAA that his party declined our invitation to participate in the protest public meeting held in Nizamabad," Owaisi said.
( With inputs from IANS )