<?xml version="1.0"?><ownershipDocument><schemaVersion>X0201</schemaVersion>    <documentType>4</documentType><periodOfReport>2004-01-01</periodOfReport><notSubjectToSection16>0</notSubjectToSection16><issuer><issuerCik>0000769644</issuerCik><issuerName>COLE NATIONAL CORP /DE/</issuerName>        <issuerTradingSymbol>CNJ</issuerTradingSymbol></issuer><reportingOwner><reportingOwnerId><rptOwnerCik>0000922594</rptOwnerCik><rptOwnerName>COLE JEFFREY A</rptOwnerName></reportingOwnerId><reportingOwnerAddress><rptOwnerStreet1>211 ESPLANADE WAY</rptOwnerStreet1><rptOwnerStreet2></rptOwnerStreet2><rptOwnerCity>PALM BEACH</rptOwnerCity><rptOwnerState>FL</rptOwnerState><rptOwnerZipCode>33480</rptOwnerZipCode><rptOwnerStateDescription></rptOwnerStateDescription></reportingOwnerAddress><reportingOwnerRelationship><isDirector>1</isDirector><isOfficer>0</isOfficer><isTenPercentOwner>0</isTenPercentOwner><isOther>0</isOther></reportingOwnerRelationship></reportingOwner><derivativeTable><derivativeTransaction><securityTitle><value>Director Stock Option (Right to Buy)</value></securityTitle><conversionOrExercisePrice><value>19.9650</value></conversionOrExercisePrice><transactionDate><value>2004-01-01</value></transactionDate><deemedExecutionDate></deemedExecutionDate><transactionCoding><transactionFormType>4</transactionFormType><transactionCode>A</transactionCode><equitySwapInvolved>0</equitySwapInvolved><footnoteId id="F1" /></transactionCoding><transactionTimeliness><value></value></transactionTimeliness><transactionAmounts><transactionShares><value>1571.0000</value></transactionShares><transactionPricePerShare><value>0</value></transactionPricePerShare><transactionAcquiredDisposedCode><value>A</value></transactionAcquiredDisposedCode></transactionAmounts><exerciseDate><value>2005-01-01</value></exerciseDate><expirationDate><value>2014-01-01</value></expirationDate><underlyingSecurity><underlyingSecurityTitle><value>Common Stock</value></underlyingSecurityTitle><underlyingSecurityShares><value>1571.0000</value></underlyingSecurityShares></underlyingSecurity><postTransactionAmounts><sharesOwnedFollowingTransaction><value>1571.0000</value></sharesOwnedFollowingTransaction></postTransactionAmounts><ownershipNature><directOrIndirectOwnership><value>D</value></directOrIndirectOwnership></ownershipNature></derivativeTransaction></derivativeTable><footnotes><footnote id="F1">Reflects the automatic award of options under the Amended and Restated Nonqualified Stock Option Plan for Nonemployee Directors, which was approved by shareholders in 1997.</footnote></footnotes><remarks></remarks><ownerSignature><signatureName>Jeffrey A. Cole</signatureName><signatureDate>2004-01-05</signatureDate></ownerSignature></ownershipDocument>

