He, however, said that the final call on the issue would be taken by BJD president and Chief Minister Naveen Patnaik.
Mr Rout made these remarks when asked by reporters about his party's position in the context of the political situation in Gujarat ahead of its upcoming Assembly elections.
"The Congress is a secular party like us. On the other hand, we have an ideological difference with the BJP. All anti-BJP and anti-communal political outfits should now come together," he said.
On whether the BJD's policy of maintaining "equal distance" from the Congress and the BJP will not be affected by it, Mr Rout, who is also the state agriculture minister, said, "We will welcome the Congress if they join us."
The BJD leader said the Congress should submit a list of Assembly segments where they are confident of winning.
Earlier, BJD's Parliamentary Party leader in the Lok Sabha Bhartuhari Mahtab had also made a similar statement favouring a tie-up with the Congress. However, Mr Mahatab's suggestion was then rejected by Mr Patnaik.
Reacting to the BJD vice president's comments, Odisha Congress chief Prasad Harichandan said, "This is Damodar Rout's personal opinion. He is a senior leader. Everybody knows the BJP is a communal party. About alliance with any other party, an AICC committee headed by AK Antony takes the decision. No such decision is taken at the state level."
"As of now, we are fighting against both the BJD and the BJP in Odisha," he said here.
Leader of Opposition in Odisha Assembly and senior Congress leader Narasingha Mishra said, "The proposal of a tie-up with us should come from the BJD president."
Meanwhile, Union minister and senior BJP leader Prakash Javadekar claimed that even if the Congress and the BJD join hands, it would not affect his party's electoral chances in the state.
"No matter what they do, two zeros cannot make a hero," he said.