Bertrand, 27, who featured for England in this week's friendly defeat to France in Paris, revealed on Twitter that he wants to help out those affected by the fire disaster by doing more than just donating.
Fifty-eight people are missing and presumed dead and Metropolitan Police Commander Stuart Cundy, the officer in charge of the investigation, has warned the death toll could rise further.
Bertrand said: "I went to Grenfell Tower (on Friday). I want to help, not just donate. I can't think of all the answers but I can do what I feel is needed.
"Starting with rehousing the victims, and making sure they don't leave the W11 post code. And remain on the emergency housing list.
"Monday I will be around RugbyPortobello putting this plan into action. From 10:30am until progress has been made."
Mr Cundy said on Saturday that of the 58 people, 30 were confirmed dead while16 bodies had been recovered from the 120-flat Tower and taken to a mortuary.
Bertrand, who won his 14th England cap in Tuesday's 3-2 defeat, signed a new five-year contract with Southampton last summer after joining from Chelsea in a £10million deal in 2015 after an initial loan spell.
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