Shares of Sears Holdings Corp. rallied 2.3% in premarket trade Tuesday, after ESL Investments Inc., which has proposed to buy certain assets of the troubled department store chain, said it has received "numerous" inquiries from potential partners in a deal. ESL, the hedge fund run by Sears' Chief Executive Eddie Lampert, said it asked Sears to reconsider the limits it has placed on ESL's ability to engage with potential partners for a deal. Since ESL made its proposal on April 20, ESL said there has been a "significant increase" in the price for Sears' unsecured debt that would make certain debt repurchases and debt-for-equity exchanges less attractive. "We wanted to emphasize that finding an appropriate partner soon will be a critical factor that will materially impact any definitive proposal that we are able to make," ESL said in a letter to Sears' board of directors. "Specifically, we believe that our ability to execute the ESL Proposal depends on our ability to engage with partners that can provide strategic and/or management experience to these businesses." Sears' stock has lost 2.5% year to date through Friday, while the SPDR S&P Retail ETF has gained 3.3% and the S&P 500 has tacked on 1.8%.