The Germanwings plane carrying 150 people crashed on its way from Barcelona to Duesseldorf.
Mr Hammond said "based on the information available to us" it was likely British nationals were involved.
But he said he would not speculate on numbers of Britons involved until checks were completed.
"We are working closely with the French, German and Spanish authorities, and the airline, to establish the facts," he said.
He also said the UK Air Accident Investigation Branch, and UK disaster victim identification experts, were standing by to offer assistance to the French authorities, if required.
One passenger on the plane was named as Marina Bandres Lopez-Belio - a UK resident originally from Jaca in Spain - by the mayor of her Spanish home town.
The mayor of Jaca, Victor Barrio, said Ms Bandres was on the flight with her baby son Julian and had been in the Spanish Pyrenees town to attend a relative's funeral.
But he said he did not know if her husband was also on the flight with her.
Ms Bandres's former school, Colegio Escuelas PÃ­as in Jaca, issued a message of "sincere condolences" to her family.
The Manchester Evening News reported that she had lived in the Fallowfield area of Manchester and Rochdale since arriving in the UK.
The Airbus A320 - flight 4U 9525 - went down between Digne and Barcelonnette.
There are no survivors, officials say.
France's interior minister said the "black box" flight recorder has been found but the cause of the crash is not yet known and the plane sent no distress signal during an eight-minute descent.
Some British nationals were "sadly likely" to have been on board the plane that crashed in the French Alps, Foreign Secretary Philip Hammond says.