<?xml version="1.0"?><ownershipDocument><schemaVersion>X0201</schemaVersion>    <documentType>4</documentType><periodOfReport>2003-08-27</periodOfReport><notSubjectToSection16>0</notSubjectToSection16><issuer><issuerCik>0001163370</issuerCik><issuerName>NORTHRIM BANCORP INC</issuerName>        <issuerTradingSymbol>NRIM</issuerTradingSymbol></issuer><reportingOwner><reportingOwnerId><rptOwnerCik>0001197405</rptOwnerCik><rptOwnerName>SWALLING JOHN C</rptOwnerName></reportingOwnerId><reportingOwnerAddress><rptOwnerStreet1>C/O NORTHRIM BANK</rptOwnerStreet1><rptOwnerStreet2>3111 C STREET</rptOwnerStreet2><rptOwnerCity>ANCHORAGE</rptOwnerCity><rptOwnerState>AK</rptOwnerState><rptOwnerZipCode>99503</rptOwnerZipCode><rptOwnerStateDescription></rptOwnerStateDescription></reportingOwnerAddress><reportingOwnerRelationship><isDirector>1</isDirector><isOfficer>0</isOfficer><isTenPercentOwner>0</isTenPercentOwner><isOther>0</isOther></reportingOwnerRelationship></reportingOwner><nonDerivativeTable><nonDerivativeTransaction><securityTitle><value>Common Stock</value></securityTitle><transactionDate><value>2003-08-27</value></transactionDate><deemedExecutionDate></deemedExecutionDate><transactionCoding><transactionFormType>4</transactionFormType><transactionCode>P</transactionCode><equitySwapInvolved>0</equitySwapInvolved></transactionCoding><transactionTimeliness><value></value></transactionTimeliness><transactionAmounts><transactionShares><value>20</value><footnoteId id="F1" /></transactionShares><transactionPricePerShare><value>18.85</value></transactionPricePerShare><transactionAcquiredDisposedCode><value>A</value></transactionAcquiredDisposedCode></transactionAmounts><postTransactionAmounts><sharesOwnedFollowingTransaction><value>20</value></sharesOwnedFollowingTransaction></postTransactionAmounts><ownershipNature><directOrIndirectOwnership><value>I</value></directOrIndirectOwnership><natureOfOwnership><value>By son</value></natureOfOwnership></ownershipNature></nonDerivativeTransaction><nonDerivativeHolding><securityTitle><value>Common Stock</value></securityTitle><postTransactionAmounts><sharesOwnedFollowingTransaction><value>1470</value></sharesOwnedFollowingTransaction></postTransactionAmounts><ownershipNature><directOrIndirectOwnership><value>I</value></directOrIndirectOwnership><natureOfOwnership><value>By LLC</value></natureOfOwnership></ownershipNature></nonDerivativeHolding><nonDerivativeTransaction><securityTitle><value>Common Stock</value></securityTitle><transactionDate><value>2003-08-27</value></transactionDate><deemedExecutionDate></deemedExecutionDate><transactionCoding><transactionFormType>4</transactionFormType><transactionCode>P</transactionCode><equitySwapInvolved>0</equitySwapInvolved></transactionCoding><transactionTimeliness><value></value></transactionTimeliness><transactionAmounts><transactionShares><value>100</value></transactionShares><transactionPricePerShare><value>18.85</value></transactionPricePerShare><transactionAcquiredDisposedCode><value>A</value></transactionAcquiredDisposedCode></transactionAmounts><postTransactionAmounts><sharesOwnedFollowingTransaction><value>600</value></sharesOwnedFollowingTransaction></postTransactionAmounts><ownershipNature><directOrIndirectOwnership><value>D</value></directOrIndirectOwnership></ownershipNature></nonDerivativeTransaction></nonDerivativeTable><footnotes><footnote id="F1">The reporting person disclaims beneficial ownership of these securities and this report shall not be deemed an admission that the reporting person is the beneficial owner of such securities for purposes of Section 16 or for any other purpose.</footnote></footnotes><remarks></remarks><ownerSignature><signatureName>/s/ John C. Swalling</signatureName><signatureDate>2003-09-02</signatureDate></ownerSignature></ownershipDocument>

