Lineker, who has hosted refugees in his home, had been suspended on March 10 for a tweet that called government policy on migration 'immeasurably cruel' and compared language used to support it to 'that used by Germany in the 30s'.
Other presenters have also pulled out of BBC appearances after former England soccer captain Lineker, who presents the flagship "Match of the Day" soccer highlights programme, was taken off air by the BBC on Friday.
Lineker was told there has to be an agreed position on his use of social media before he can return, the BBC said on Friday, with Director General Tim Davie saying it had taken a "proportionate action".
The motion, moved by BJP MLA Vipul Patel of Sojitra constituency, seeks recommendation to the Centre for action against the media house.
Last month, India's tax authorities conducted searches at the BBC offices in New Delhi and Mumbai.
Tim Davie sent an email to the staff in which he said the broadcaster was 'driven by purpose'.
Motson went on to cover 10 World Cups, 10 European Championships and 29 FA Cup finals for the BBC before retiring from the organisation in 2018.
We stand up for the BBC. We fund the BBC. We think the BBC World Service is vital. We want the BBC to have that editorial freedom, said David Rutley, Parliamentary Under-Secretary of the FCDO.
The BBC has published its response to the three-day IT 'survey' on its Hindi website.
The Central Board of Direct Taxes said its survey revealed that income/profits shown by various group entities were not commensurate with the scale of operations in India.