I am not sure if I understand your question fully. The linker region, or the fusion peptide, can be hydrophobic or hydrophilic. This choice depends on what you want to achieve. In most cases you want to build in some flexibility so the two protein parts can interact freely. If you have a hydrophobic linker this will have a tendency either to be inserted into the interior of the protein, to cause protein aggregation or be inserted into a cellular membrane. This latter effect is simply caused by the hydrophobic character of lipid bilayers.

As I read your question, you are talking of proteins that assist in the fusion of two membranes, such as snares (VAMP) or HIV GP41, not of protein design fusion of two protein domains as Leif Bülow assumed.

If you look at the wikipedia article on snares (https://en.wikipedia.org/wiki/SNARE_(protein)), one part of the snare protein has to transverse the membrane, then you have a short hydrophilic stretch interacting with the polar headgroups of the membran lipids, then a hydrophobic leucine zipper where the hydrophobic side of the helices interact to form a 4-alpha-helix bundle that shields the hydrophilic segment from the solvent. See Article The Multifaceted Role of SNARE Proteins in Membrane Fusion

Thank you Leif Bülow and Annemarie Honegger. Your views have helped me so much because initially I was confused how a hydrophobic protein would interact with the target host cell lipid bilayer.