<?xml version="1.0"?><ownershipDocument><schemaVersion>X0201</schemaVersion>    <documentType>4</documentType><periodOfReport>2003-12-15</periodOfReport><notSubjectToSection16>0</notSubjectToSection16><issuer><issuerCik>0001163370</issuerCik><issuerName>NORTHRIM BANCORP INC</issuerName>        <issuerTradingSymbol>NRIM</issuerTradingSymbol></issuer><reportingOwner><reportingOwnerId><rptOwnerCik>0001188779</rptOwnerCik><rptOwnerName>MOLLOZZI VICTOR P</rptOwnerName></reportingOwnerId><reportingOwnerAddress><rptOwnerStreet1>3111 C STREET</rptOwnerStreet1><rptOwnerStreet2></rptOwnerStreet2><rptOwnerCity>ANCHORAGE</rptOwnerCity><rptOwnerState>AK</rptOwnerState><rptOwnerZipCode>99503</rptOwnerZipCode><rptOwnerStateDescription></rptOwnerStateDescription></reportingOwnerAddress><reportingOwnerRelationship><isDirector>0</isDirector><isOfficer>1</isOfficer><isTenPercentOwner>0</isTenPercentOwner><isOther>0</isOther><officerTitle>SVP, Senior Credit Officer</officerTitle></reportingOwnerRelationship></reportingOwner><nonDerivativeTable><nonDerivativeTransaction><securityTitle><value>Common Stock</value></securityTitle><transactionDate><value>2003-12-15</value></transactionDate><deemedExecutionDate></deemedExecutionDate><transactionCoding><transactionFormType>4</transactionFormType><transactionCode>S</transactionCode><equitySwapInvolved>0</equitySwapInvolved><footnoteId id="F1" /></transactionCoding><transactionTimeliness><value></value></transactionTimeliness><transactionAmounts><transactionShares><value>5175.0000</value></transactionShares><transactionPricePerShare><value>23.0100</value></transactionPricePerShare><transactionAcquiredDisposedCode><value>D</value></transactionAcquiredDisposedCode></transactionAmounts><postTransactionAmounts><sharesOwnedFollowingTransaction><value>24798.0000</value></sharesOwnedFollowingTransaction></postTransactionAmounts><ownershipNature><directOrIndirectOwnership><value>D</value></directOrIndirectOwnership></ownershipNature></nonDerivativeTransaction></nonDerivativeTable><footnotes><footnote id="F1">Disposition of shares acquired in option exercise and related payment of already owned Northrim shares as reported on Form 4 statement dated December 10, 2003 to,in part, pay taxes.</footnote></footnotes><remarks></remarks><ownerSignature><signatureName>/s/ Victor P. Mollozzi</signatureName><signatureDate>2003-12-15</signatureDate></ownerSignature></ownershipDocument>

