The primary cell surface receptor for SARS-CoV-2 is the angiotensin-converting enzyme 2 (ACE2). Recently it has been noticed that the viral Spike protein has an RGD motif, suggesting that cell surface integrins may be co-receptors. We examined the sequences of ACE2 and integrins with the Eukaryotic Linear Motif resource, ELM, and were presented with candidate short linear motifs (SLiMs) in their short, unstructured, cytosolic tails with potential roles in endocytosis, membrane dynamics, autophagy, cytoskeleton and cell signalling. These SLiM candidates are highly conserved in vertebrates. They suggest potential interactions with the AP2 mu2 subunit as well as I-BAR, LC3, PDZ, PTB and SH2 domains found in signalling and regulatory proteins present in epithelial lung cells. Several motifs overlap in the tail sequences, suggesting that they may act as molecular switches, often involving tyrosine phosphorylation status. Candidate LIR motifs are present in the tails of ACE2 and integrin beta3, suggesting that these proteins can directly recruit autophagy components. We also noticed that the extracellular part of ACE2 has a conserved MIDAS structural motif, which are commonly used by beta integrins for ligand binding, potentially supporting the proposal that integrins and ACE2 share common ligands. The findings presented here identify several molecular links and testable hypotheses that might help uncover the mechanisms of SARS-CoV-2 attachment, entry and replication, and strengthen the possibility that it might be possible to develop host-directed therapies to dampen the efficiency of viral entry and hamper disease progression. The strong sequence conservation means that these putative SLiMs are good candidates: Nevertheless, SLiMs must always be validated by experimentation before they can be stated to be functional.