They include sending investigators disguised as patients to uncover fraud and waste in existing healthcare plans for the poor and elderly.
The second is the proposed expansion of pilot programmes to bring more predictability to medical malpractice lawsuits.
Others include increasing payments to providers in the medicaid programme for the poor and expanding the use of health savings accounts.
"Merely incorporating these ideas into the deeply flawed House and Senate bills will not bring us any closer to real reform"
Tom Coburn, a Republican senator
Obama's letter said: "I said throughout this process that I would continue to draw on the best ideas from both parties, and I'm open to these proposals in that spirit."
But he again rejected Republican appeals to restart the healthcare debate or dramatically scale back his proposals.
"Piecemeal reform is not the best way to effectively reduce premiums, end the exclusion of people with pre-existing conditions or offer Americans the security of knowing that they will never lose coverage," Obama's letter said.
Mitch McConnell, a Senate Republican leader, warned that Democrats will enact their healthcare plan at their own political peril, vowing to make it an issue in every congressional race this November.
Senator Tom Coburn, a Republican who proposed some of the notions Obama is weighing, said: "Merely incorporating these ideas into the deeply flawed House and Senate bills will not bring us any closer to real reform."
Budget reconciliation rules
Obama was expected to reiterate why changing the system is so important and again explain what his plans would mean to families and businesses.
The president's aides also expected Obama to talk about the Republican ideas he wants woven into the Democrats' plans.
He is expected to leave no doubt that, barring an unexpected change in Republican tactics, he wants Congress to pass the legislation using budget reconciliation rules.
Those rules prohibit filibusters, which are delaying tactics meant to stall legislation. It takes 60 votes to halt a filibuster, and Democrats control only 59 in the 100-member Senate.
Obama is unlikely to use those exact words, as Democratic leaders are emphasising they want to pass a bill with simple majority votes in the Senate and House of Representatives.