<?xml version="1.0"?>
<ownershipDocument>
    <schemaVersion>X0201</schemaVersion>

    <documentType>4</documentType>
<periodOfReport>2003-10-01</periodOfReport>
<notSubjectToSection16>0</notSubjectToSection16>
    <issuer>
        <issuerCik>0001219702</issuerCik>
        <issuerName>LINK ENERGY LLC</issuerName>
        <issuerTradingSymbol>LNKE.OB</issuerTradingSymbol>
</issuer>
<reportingOwner>
        <reportingOwnerId>
            <rptOwnerCik>0001263482</rptOwnerCik>
            <rptOwnerName>GIBBS DANA R</rptOwnerName>
        </reportingOwnerId>
        <reportingOwnerAddress>
            <rptOwnerStreet1>2000 W SAM HOUSTON PKWY S</rptOwnerStreet1>
            <rptOwnerStreet2>SUITE 400</rptOwnerStreet2>
            <rptOwnerCity>HOUSTON</rptOwnerCity>
            <rptOwnerState>TX</rptOwnerState>
            <rptOwnerZipCode>77042</rptOwnerZipCode>
            <rptOwnerStateDescription></rptOwnerStateDescription>
        </reportingOwnerAddress>
            <reportingOwnerRelationship>
<isDirector>0</isDirector>
<isOfficer>1</isOfficer>
<isTenPercentOwner>0</isTenPercentOwner>
<isOther>0</isOther>
<officerTitle>President and CCO</officerTitle>
<otherText></otherText>
</reportingOwnerRelationship>
</reportingOwner>
<nonDerivativeTable>
<nonDerivativeTransaction>
<securityTitle>
<value>Link Energy LLC (common units)</value>
</securityTitle>
<transactionDate>
<value>2003-10-01</value>
</transactionDate>
<deemedExecutionDate>
</deemedExecutionDate>
<transactionCoding>
<transactionFormType>4</transactionFormType>
<transactionCode>A</transactionCode>
<equitySwapInvolved>0</equitySwapInvolved>
</transactionCoding>
<transactionTimeliness>
<value></value>
</transactionTimeliness>
<transactionAmounts>
<transactionShares>
<value>85000</value>
<footnoteId id="F1"/>
</transactionShares>
<transactionPricePerShare>
<footnoteId id="F1"/>
</transactionPricePerShare>
<transactionAcquiredDisposedCode>
<value>A</value>
</transactionAcquiredDisposedCode>
</transactionAmounts>
<postTransactionAmounts>
<sharesOwnedFollowingTransaction>
<value>85160</value>
</sharesOwnedFollowingTransaction>
</postTransactionAmounts>
<ownershipNature>
<directOrIndirectOwnership>
<value>D</value>
</directOrIndirectOwnership>
<natureOfOwnership>
<value></value>
</natureOfOwnership>
</ownershipNature>
</nonDerivativeTransaction>
</nonDerivativeTable>
<footnotes>
<footnote id="F1"> (1) This restricted unit award is subject to the following vesting restrictions: (i) 50% on June 1, 2004, and (ii) 25% on each of June 1, 2005 and 2006.</footnote>
</footnotes>
<remarks></remarks>
<ownerSignature>
<signatureName>John D. Zimmerman, POA</signatureName>
<signatureDate>2003-10-03</signatureDate>
</ownerSignature>
</ownershipDocument>

