The British premier will meet Martin Schulz and leaders of the two main political groups in the assembly, hoping to find a sympathetic ear over reforms he is demanding to avoid a so-called “Brexit” from the 28-member bloc.
European Union chief Donald Tusk on Monday said the EU was at a “critical moment” in its history, warning during a visit to Romania that “the risk of break-up is real because this process is indeed very fragile”.
Britain has been pushing for a change to EU rules, including limiting welfare benefits for migrants and to protect countries that do not use the euro, ahead of an “in-out” referendum expected in June.
Downing Street indicated a deal on the reforms is expected at a summit on Thursday and Friday, after Cameron held last-minute talks with French President Francois Hollande.
They “agreed that we are making good progress on the UK renegotiation and that the draft text from the European Council provides a firm basis to reach agreement at this week’s summit”, the prime minister’s spokesman said after the talks in Paris on Monday.
The upbeat assessment came after a French official warned earlier in the day that while there was “political willingness” to clinch an agreement, “more work is needed, particularly on economic governance”.
The EU is already grappling with the biggest migration crisis in 70 years and signs the sluggish eurozone economy could once again be stalling.
Debate over Britain’s future in the bloc has also struck a political nerve, with heavyweight France reportedly concerned about protections London is demanding for members that do not use the single currency.