Paul and Rachel Chandler, aged 58 and 55, of Tunbridge Wells, Kent, were heading for Tanzania in their yacht, the Lynn Rival.
They sent a distress signal on Friday but have not been heard from since.
BBC security correspondent Frank Gardner said his sources believed they were being taken to Somalia.
He said it was thought the couple and their yacht were headed for the port of Haradheere.
A pirate called Hassan told the Reuters news agency: "The British couple are in our hands now. We captured them as they were touring in the Indian Ocean."
The two captives were healthy and ransom demands would follow, he added.
A Foreign and Commonwealth Office spokeswoman said it could not confirm whether pirates were involved.
"We are in touch with the family in the UK and the Seychelles coastguards which continues to monitor the situation and has conducted a search of the area," she added.
Britain's Maritime and Coastguard Agency (MCA) said the couple's distress beacon was activated at 2300 BST on Friday.
They were on a 150 nautical-mile passage south-west to the Amirante Islands, en route to Tanzania when they used the Emergency Position Indicating Radio Beacon (EPIRB).
The route would have taken the couple near Somali waters which are notorious for pirate attacks on ships and smaller boats.
It is understood that there had been pirate activity in the area earlier in the day.
A MCA spokesman said: "The Seychelles authorities are carrying out a search and rescue operation but have found nothing so far.
"It would appear from the activation of the EPIRB that something has happened.
Seychelles Coast Guard spokesman
"We were aware that the EPIRB had gone off, talked to the Seychelles, asked if they were aware of it, they were, and have been searching, by air and sea."
A spokesman for the Seychelles Coast Guard said they had not heard from the couple, who were out of reach by satellite phone.
He said: "There have been reports that they were hijacked by pirates but no one can prove that. We don't know what has happened and cannot speculate."
In recent years the waters around the Seychelles have become a hot spot for pirate activity.
Earlier this year Seychellois officials requested help from the international community to defend their waters.
The couple - who have been sailing around the world for several years after selling up in the UK - previously wrote of "the Somali pirate problem" that delayed other voyages to Tanzania.
In an earlier post on their blog, the couple wrote about pirates around the Seychelles.
They said in June: "Arriving back at the old port we had to pass three warships at the entrance, one French, one American and one Canadian. No doubt they are here to deal with the pirates.
"We also understand that the problem has gone away with the arrival of the SE winds. The seas around the Seychelles are now too rough for the pirates to operate in."
Published: 2009/10/27 11:06:41 GMT
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