On Wednesday parliament's plenary session will discuss the European council conclusions of 25-26 June 2015, as well as Tuesday's euro summit and the current situation in Greece.
Commission president Jean-Claude Juncker will be in parliament that day and Verhofstatdt has also asked that eurogroup president Jeoren Dijsselbloem be present for the Greece discussions.
The Belgian ALDE leader, said, "The ball is in the court of prime minister Tsipras. He has to explain the steps he will undertake to keep Greece in the eurozone. The referendum has made it clear that the current bailout plan is rejected, but we still do not know what measures Tsipras will propose instead."
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"The negotiations behind closed doors have failed. Now it is time to take a different approach. We need transparent negotiations in which all players show their cards.
"If Tsipras is serious about staying in the eurozone and reforming Greece, I expect to see him in the European parliament this Wednesday."
Verhofstadt's comments were echoed by Alliance of Socialists and Democrats leader Gianni Pittella, who said, "We expect the Greek government to come back to the negotiations with a renewed responsible attitude."
The Italian Socialist also called for the re-opening of "negotiations inspired by a new attitude of solidarity and cooperation, taking into account the difficult social dimension in Greece".
"We will keep on doing all that is needed to work for a reasonable and long-lasting compromise, and to prevent any possible unfortunate option of Grexit," he added.
The plenary session backed Verhofstadt's suggestions and parliament president Martin Schulz will extend an invitation to both Tsipras and Dijsselbloem.