He will attempt to change May's mind on leaving the customs union after a disastrous election in which the government lost its majority last Thursday, the newspaper said.
Brexit talks will begin Monday.
The comments added to signs that Hammond is trying to revive his calls for a business-friendly Brexit.
But May, weakened by her election flop, opted to keep Hammond in his job along with other key ministers.
Mr Hammond had been due to give at speech at Mansion House in the City of London on Thursday, and there had been speculation he would set out his vision for a "soft" Brexit - which could mean the United Kingdom retaining closer ties to the single market and possibly remaining within the customs union.
Hammond said Britain's position had been set out in a speech by May in January and a letter she sent to European Union leaders in March when she triggered the Brexit process.
Hammond's comments Friday come a day after he cancelled a keynote address to London financiers in the wake of the Grenfell Tower disaster, in which the death toll is expected to rise from 17.
"My clear view and I believe the view of the majority of people in Great Britain is we should be protecting jobs, protecting economic growth and protecting prosperity", Chancellor of the Exchequer Hammond said as he arrived for regular talks with his European Union counterparts in Luxembourg. Two former Conservative prime ministers have also urged May to soften her approach.
Labour MPs and pro-European Tories have reportedly been holding private talks to discuss how bills might be amended to keep the United Kingdom inside the customs union and leave open the possibility of staying in the single market.
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