Bushehr is Iran's only operating nuclear power plant and uses Russian fuel that Russia then takes back when it is spent to reduce proliferation risk.
The comments come amid discussions for a nuclear deal with Tehran.
In a post on Truth Social, Trump said that he believed that Putin agreed that Iran should not have a nuclear weapon.
Iran is increasingly seeking to be part of this new world order, in which non-Western countries work together against America and the West.
Iran's goal is to have China, Russia, and even some European countries potentially help it hedge against any fallout should the US talks collapse.
"Putin's trip to Tehran is currently being worked out, preparations are underway," Mohajerani was quoted as saying by RIA.
Tehran has approached the talks warily, doubting the likelihood of an agreement and suspicious of Trump, who has threatened to bomb Iran if there is no deal.
Moscow may think that it can link a Ukraine deal to a deal that will also help Iran.
Iran doesn’t have a very large navy. The importance is largely related to coordination with China and Russia.
The exercise includes drills on striking maritime targets, damage control, and joint search-and-rescue operations.