Do you have a free hydroxy or carboxylate group?

Yes I have a free hydroxyl group at the chain end of the polymer.

Try coupling with ynoic acid via DCC or EDCI

dissolve Poly(l-lactide) and sodium hydride in 1:1.2 mole ratio in dry THF solvent at zero degrees Celsius. stir the reaction mixture for 1 hour. Add propargyl bromide dropwise to the mixture for half-an-hour through syringe at room temp. stir the reaction mixture for 24 hrs. add dist. water (equal amount to THF) to quench the reaction.Add diethyl ether to the reaction mixture. collect upper layer of diethyl ether and evaporate solvent. collect the product.

If I use sodium hydride, will it not abstract the alkyne proton? @Sasidhar Kantheti

You can follow sasidhar's procedure.. There won't be any problem with the mentioned mole ratio of sodium hydride..