"I think the squad is good enough to take us from the bottom but we need some players that can improve the team," former Chelsea boss Grant said at a news conference.
"We are bottom of the league. It's a big challenge. I think we deserve to be in the Premier League."
Grant, who joined the club for a second spell as director of football in October, will replace the sacked Paul Hart as manager once his work permit has been changed.
"I think what is here is enough to stay in the division if we do the right things," the Israeili added.
Asked what the right things were, he said: "I mean win games."
Portsmouth chief executive Peter Storrie said he hoped Grant's new role would be formalised by next week, and added that the transfer ban imposed on the club was being dealt with.
"My understanding is that there will be money available and Avram will look now at where he thinks needs strengthening," Storrie said.
"I am sure he has got some names in mind ... Frank Lampard, Drogba," he joked.
Portsmouth host second-placed Manchester United on Saturday. The last time United boss Alex Ferguson came up against Grant, then manager of Chelsea, was in the 2008 Champions League final in Moscow.
Hart was sacked on Tuesday after two league wins from 13 this season.
