A lifeboat crew and a Border Force patrol vessel were called out to intercept the large rigid hulled inflatable with an enclosed cabin at the back of it.
One witness said he saw at least one child, a boy who looked about six years old and was accompanied by a woman.
According to local reports, the boat could have contained as many as 35 migrants.Coastguard and Border Force officials have been working together to bring the group to shore before they are quizzed.
It is understood one group of people has been brought ashore, given blankets and put into vans by Border Force officials on the harbour at Dover, Kent.
Hundreds of migrants, mostly Iranian, have made perilous trips across the Channel in recent months.
The incident comes after 10 suspected migrants were picked up in a RHIB near Dover in the early hours on Friday.
That was the first time migrants are thought to have made the journey across the Channel since January 21, when a group of 23 were found in two separate incidents.
More than 300 migrants have now crossed the Channel to arrive in Britain since the beginning of November.
In December, Home Secretary Sajid Javid said the dramatic spike in migrants arriving on beaches in Kent was a ‘major incident’.
On Christmas Day alone, 40 people in five boats arrived at beaches near Dover, and a further 39 arrived over one weekend in January.
Dover and Deal MP Charlie Elphicke said: 'This underlines yet again why we urgently need air surveillance day and night along the French coast - to catch the traffickers long before they reach Dover.
'If we fail to stop people attempting dangerous crossings in small craft - we risk a tragedy in the English Channel.'
A Coastguard spokeswoman said today: 'We are currently assisting Border Force with an incident off the Kent coast.'HM Coastguard is committed to safeguarding life around the seas and coastal areas of this country.
'We are only concerned with preservation of life, rescuing those in trouble and bringing them safely back to shore, where they will be handed over to the relevant partner emergency services or authorities.'
